*Cracks the knuckles*
If we take for granted that humans are an evolutionary product, and nothing more, and that intelligence is favored, if only partially, by evolution then it makes no sense for humans to be the only intelligent species to have evolved on Earth.
We aren't. Or at least, may not be. Certain cetaceans, some of the great apes, elephants, and perhaps octopi, corvids, and african grays all pass the bar of having at least 1st Order theory of mind, and possibly 2nd. In fact, dogs might even. It is just very difficult for us to recognize intelligence in another species with whom we cannot readily communicate. We have a... Cartesian Problem.
Here is the problem. Your assumptions. In order to change the focus of the Drake Equation, you had to add an assumption, namely that evolution favors intelligence. It does not, anymore than it favors webbed feet. It depends on the phylogenetic history of the organism, the ecological problem needing solved by blind tinkering, and physiological constraints on things like brain size and structure. For example, birds are capable of evolving rather impressive intelligence because flight and their evolutionary history as archosaurs pre-adapt them for it. To save weight, their neuron density is very high, they have to have a complex flight computer in there (so to speak) and they have had an well-developed social system since before they were birds.
Point being, some organisms have it easier than others when it comes to evolving intelligence, but there are still constraints. Energy intake, reproductive mode etc. For example, the head of the fetus having to get through the birth canal, which can only get so wide before females cant walk effectively, constraining brain size. We cannot have babies that are much more premature for example--and yes, all human babies are essentially preemies--and still have a decent chance of survival. So unless we re-organize our brains (fat chance), our intelligence is capped.
Other organisms have the same basic problem.
So we should not see a proliferation of technological civilizations on our one planet. Hell, out intelligence took 65 million years to evolve (I am starting at the genetic divergence of the mammalia (which is not their ecological divergence) in the late cretaceous). It required pre-adaptation by way of primate social systems, and a combination of rapidly changing physical environments and a Machiavellianity positive feedback loop to get us here.
The Drake Equation (and thus Fermi's Paradox) relies on the vast number of star systems and subsequent planets to get to the conclusion that there are extraterrestrial technological civilizations. Evolution does not need to favor anything.
This is the sort of answer that has its head so far up the ass of anthropocentrism that it loses all perspective. Hominids have tool using intelligence, that's fine but I think irrelevant. In the grand scheme of things we're part of that hereditary group and thus I lump their experiences, or at least 'our' direct ancestors' experiences, in with 'our' experiences. What you're missing is that that hominid line took about four million years to get to this point (in fact I think it took far shorter, we can see all sorts of examples of non-human tool building and language use in contemporary species. The question, I think, is the development of the cultural, dare I say memetic, passing on of the skills of tool, in which case the distinction I'm probing here is not biological but social and dates back in the tens of thousands of years.), in the biological history of Earth that goes back 500 millions that's nothing. Why didn't other species to develop?
You are missing his point. That social intelligence that permits the cultural transmission of tool use and design (for example) did not take tens of thousands of years. It took 65 million (see above). Why? Because for that to evolve, myriad other things have to evolve first within the lineage in question. It is not the cultural transmission of information you need to concern yourself with. It is the brain that is structured in such a way and large enough (for a given neuron density) that such a thing can evolve in the first place.
Or, let me boil this down even more. Hominids have developed for 60 million years (give or take) since the K-T event essentially reset most biological life on Earth.
No. It didn't. It opened the ecological niches for anything with a mass over about 25 kilos (with some leeway for larger things that could A) hide and B) survive in near-freezing temperatures with little food for years. Essentially, crocodilians and large ectothermic burrowing or aquatic reptiles, as well as sharks were the only large things that passed through the selective filter of the KT event). What filled those niches were things that were most rapidly able to take them over due to chance pre-adaptation. For example, sharks re-radiated to fill most of the aquatic predator niches left by mosasaurs and the non-croc archosaurs, because they were already there. Mammals had already differentiated into a wide variety of species by the time the KT event happened. They were not "reset". Their evolutionary histories and the constraints and pre-adaptations flowing therefrom were not erased.
The Mesozoic period, by contrast, saw roughly 150 million to 200 million years of more or less stable development of life after the Permian-Triassic extinction event until the K-T event.
No. It did not. There was another extinction event resulting from the breakup of Pangea and the subsequent titanic volcanism in the late triassic that wiped out 70% of all animal and plant life, and allowed the dinosaur branch of archosaurs to take over most terrestrial niches. Prior to that, the species compliment of earth was the stuff that survived--mostly by chance--the not-even-selective filter of the permian extinction. This included archosaurs, early dinosaurs, mammal like reptiles etc.
There was another (smaller and more gradual) extinction event brought about by a climate shift between the Jurassic and Cretaceous that did things like take out Stegosaurs and cut down Sauropod diversity.
Given our contemporaries it's fair to say that at least a degree of intelligence, communication, and tool use must have existed. So why do we not have evidence of a dominantly intelligent species during the Mesozoic period? Nothing in your answer touches on this.
The answer... is because you are full of shit.
If life has existed for three hundred to four hundred million years I think it is the height of human exceptionalism to say that the sort of accrual of skills and knowledge that has led to modern hominids and humans could have occurred in recent history.
*sigh*
Cultural knowledge transmission is not limited to humans, or even for that matter to primates. However, the reason we dont see evidence of reptile overlords of the world is that non existed. This is not to say that some of the therapods were not very clever (Troodon and the other raptors come to mind), and culturally transmitted information to their offspring. But a human-level intellect is not a thing that evolves just because it might be nice to have. In much the same way that just because it would be nice for a little pond turtle to be able to lay more and larger eggs, does not mean such a thing can evolve due to space limitations inside the shell.
Simply put, a favored trait (be it reproductive rate, or intelligence) will evolve until the benefit (in fitness) is equal to the cost of that trait--and that is for each marginal increase. Evolution cannot look ahead and decide "hey, the ability to do calculus would be useful!". It has to work incrementally. This (as mentioned above for things like fetal head size, and moms pelvic girdle) applies to humans, like it does for everything else.
The climate was stable
No. It was not. It was unstable over long time scales, too long for evolution to act upon. Actually, short time scale climatic instability is one the reasons we have the intelligence that we do--the ability to solve problems in an unpredictable environment is something evolution can work with.
there was certainly enough competitive impetus, braid development had occurred and we know from nesting sites that was social interaction throughout most of the time frame
Those are necessary but not sufficient conditions. See above regarding costs. The generation by generation marginal fitness benefit must outweigh the costs. For example, there is a limit to how large a structure like the brain can grow in an enclosed space. Dinosaurs had precocial offspring--they were developed enough to move about on their own very shortly after they hatch. This requires a well developed skeletal system etc. With their pre-existing brain structure they would need a brain case larger than what they had to produce human levels of intellect, which would need to fit inside an egg, which would necessarily take away space from other structures. There are two ways to solve this problem. Development can occur post hatching--in which case, mom is stuck taking care of completely helpless offspring for weeks or months, as opposed to looking after well developed ones-- or the egg can get larger. A larger egg means fewer eggs, and it may run into hard size limits on oviposition, egg strength, diffusion of oxygen etc. Then there are the energetic costs of an energy sucking brain. Thermoregulation for a large brain. Space limitations in the brain case that might impede other structures like the development of the olfactory bulb or inner eat if the dino equivalent of a neo-cortex (it would not be a neo-cortex) were to evolve. Birds solve this to some extent (and presumably pre-dates them i therapods somewhat) bu having a really high density of neurons, but even they run into limits due to the axon-->dendrite structure of vertebrate neural connections (which incidentally is not common to inverts. One of those early divergence things. An insect brain can do more with less because of the way their neurons are connected to eachother)
Given that it'd require very strong evidence to prove to me it didn't happen, so why don't we have evidence of it?
Other than what I just laid out because you dont know how evolution and development work?
Burden of proof fallacy, appeal to ignorance. Those are your failings (some of them, anyway).