Since your argument is basically on utilitarian grounds (benefit to more) rather than deontological principles (sanctity of property or body), how would you like it if the government puts $10000 in your pocket as "compensation" then rips off one of your eyes, one of your kidneys, half your liver, one of your ears, one of anything else you have a double of and half of anything that you only "need" half of.
You are still more or less functional and $10000 richer. The half-liver and kidney went to two people, your eye went to make one totally blind guy see again, and so on. Mathematically it is valid utilitarian math.
Do you really think that's a "Utilitarian" solution to be adopted to society?
WHen you are talking about living people, they are preferences. Those people can feel, can think, and can experience. There really are no qualifiers above, so I assume anyone could be the target of this. This would not only affect the people you are taking from directly, it would also have indirect long term consequences. Yes, you are functional with one eye. To an extent. The same can be said of other organs you only really "need" one of, but what sacrifice of the individual is worth another's?
Forcibly taking organs from the unwilling living is very different from taking the organs of dead people. The dead have no preferences at all and you can't objectively hurt them or violate any of their preference. They can't suffer at all, and no one really need suffer or worry about themselves indirectly, since you are only dealing with dead people anyway. A living person down the road has no need to fear for his life and or suffer in fear of being hacked to pieces if you take the dead. The same cannot be said of the living "donors."
The above proposal could actually, on the macro level, cause less Utility to society and backfire horribly. You have to ask: "Is this the MOST necessary means to achieve the goal, and what are the long and short term consequences of it." Sometimes, Act Utilitarianism can lead to many problems on the macroscale if the particular action were to set a dangerous precedent (when applied consistently as a moral maxim). What you are suggesting is very similar to the "hospital" scenario anti-utilitarians come up with. That scenario claims that, mathematically, you could potentially save many lives by hacking up one healthy guy who comes into the hospital (yet leaving him technically functional). THere is also a version where you kill him and harvest his organs. However, it does not take long-term macro-problems into calculation. Sure, directly, it might have that potential to improve the lives of many people from the cost of fewer individuals, but at what cost to society/family and associates? Is it applicable? What cost is it to the individual as well? You would also have to measure what preferences the hosts would lose compared to those their recipients would gain.
I'm pretty sure people in society, if this is made a moral maxim of general conduct, are't going to be fine with you going around to live people and disassembling them for spare parts. From a Rule-perspective, this would not work on Utilitarian grounds. The paranoia and fear that would likely erupt due to the government seizing random people who are still alive and ripping off their body parts would be something which you couldn't reasonable deal with and keep society free, stable, and happy.
Anyone can be a target, so it will likely create mass fear to live in a society that can take anyone, any time, and hack them up for part (but leave them functional).
It would also probably not be the only means to achieve a similar goal. Sometimes, Utility is a lot more than a simple numbers game. Even if we assume it is a morally 'fair trade" on the individual level and in the Act Utilitarian framework, the macro consequences can nix it if society can't function well after it's consistent application. I can't see society working while everyone is worrying when the goverment will come and hack them into pieces for others.