It might be helpful if we started making distinctions about what sort of threat and damage people expect fighters to do against capital ships (and the kinds of capital ships.) I could join the whole "cite a specific source" bandwagon (If you're curious, both EGV&V for example portray the TIE bomber as a precision/surgical bomber for space and ground targets.) or point out how they're deployed in movies, TV, or books (which varies depending on the source, you can find at least one example for any argument.) but that will just lead to more endless argument over whose sources are better.
Now, fighters and bombers could do lots of kinds of damage, ranging from "taking out gun turrets/sensors/comms/shield arrays" (even fighters could in theory do this in the right circumstnaces) to "blasting capital ships to pieces" - often with salvoes of heavy warheads (although usually I remember they were only crippled and not outright demolished.) Now, even if you pick a specific example along that range as general, there are still lots of variables: are we talking the Imperial military at its height, or are we talking about the Imperial Warlords? Ship condition matters alot and alot of factors can alter that - access to logistics and supply lines, whether or not you have important, front-line combat ships or are stick with older (or perhaps outdated/decomissioned) ships, political factors (politics plays a HUGE role in the Imperial Military, as Tarkin demonstrates.) and so on. Ships are complicated devices, with lots of potential failure points. In some cases, like with the Warlords, its quie possible ships aren't as well maintained and prone to failures at times of stress (a point even made in Bacta War I recall with ISard's forces on Thyferra.) Ship quality is also an issue. Just because its a wedge shaped vessel doesnt neccesarily mean its a top of the line warship. Who builds it, how its armed, what sort of powerplant they stuck in it, etc. all matter - there are LOTS of Star Destroyer types and variants of a particular type.
Even beyond that, there is the issue of the technology. As I have pointed out before, there are ample evidence for devices which allow for objects to negate, weaken, or otherwise bypass shielding. Torpedo sphere proton torpedoes, the Galaxy gun missiles, Black Fleet Crisis plasma torpedoes, Individual field disruptors (Pondo Baba/EVazen short story IIRC correctly), the assassin drone that attacked Amidala in AOTC, etc. The technology, if it exists, probably is not static - there likely try to find ways to defeat shields while shield designers find ways to prevent such attacks from bypassing the defense (after all, if shields became totally nullified, who would bother using them?) Hell, fighters might even employ such technologies (Implied to be so in the ANH radio drama, although that is complicated by whether you take the "magentic field" to be the outer shields, or factor the novelization depiction into the radio drama depiction... damn inconsistencies.) which could explain the "getting close" bits we see so often.
So before deciding which sources are right or not, perhaps we could decide what it is we think fighters and bombers ought to be capable of doing to ships (and what kind of ships, and in what state, and so on?)
Purple wrote:
Could it be that, operating on a limited budget and under doctrinal limitations from the few people that were pushing for a different approach the Imperial Navy simply did not have enough resources to go around. And once they spent all that money on the shiny new star destroyers they needed a cheap fighter to fill the gap. Something similar to the reasons why Germans newer did heavy bombers in WW2.
It need not even e that complicated or extreme. Simple politics could dictate that the allocation of funding to the military is less efficient or extremely skewed. There were military and corporate interests (like KDY) who disliked the Death Star project and kept out of it, or the Adrmials who opposed Vader's building of the Executor, or Rohm Moc's Darktrooper project... I could go on. Tarkin was a very political animal, and a very influential one at that (with his own pet military officers as well, like Motti) and he could use his position and authority to requisition stuff for his own schemes. I imagine if Tarkin did it, lots of other Imperial officials did (another smaller example was that Gurdrun guy from the IG-88 story.)
When you get down to it, the Imperial Navy is just as political as any other segment of the Empire, with all the problems and restrictons that puts on things. That may even be one factor why palpy favored the Death STar - there is evidence that while he expanded and glrofied the fleet, he did not wholly trust it (There was inter-service rivarly, such as the disputes between the "generationals" - naval familes serving since the time of the Republic, and Palpy's own supporters/appointiees to the military. And the Army vs Navy rivalry, the rivalry between those two and COMPSEC, the Stormtroopers, etc.) Anyhow if Palpy didn't want to rely too heavily on the Navy, he probably wouldn't want to expand it too much unless he could keep absolute control of it (Death Stars would be easier to keep control of, in theory.) I suppose in practice its a "we got nukes so why do we need a military" mentality when it comes to deterrence and such.
And here I thought it was the capital ships of the Rebel-Alliance, that were responsible for the shield-loss of Executor. From the ROTJ-novel: 
