My main gripe is, I guess, that there seems to be something deeply right in what the Kantians and Aristotelians are saying as well. We do, like Kantians, seem to think of morality as consisting in part of rational, exceptionless rules regarding behavior. We also, like Aristotleians, seem to think that morality consists at least in part in the acquisition of certain traits and the fulfillment of certain roles.
It's very compelling, and in certain cases, such considerations have to be taken into consideration when framing social policies. For instance, if any substantial part of the society hold such beliefs passionately, then imposing some framework, top-down, that the majority doesn't accept is going to lead to perceived illegitimacy and any presumed advantage to doing so stands a chance of being wiped out by the backlash.
Then you lead to the situation where the goal is seen as so desirable that the solution is simply to get rid of those people. This may "work," even in the long run, although it usually doesn't. If you consider China moving from an impoverished, backward society continually exploited by every great power in the world working in tandem to a modern, industrial, horribly polluted, half-totalitarian dystopia in a few decades an improvement, that would be an example.
However, if you still reject any outcome like that, it is easy enough to reject any policies that kill innocent people, or at least result in an unacceptable level of deaths. (For instance, despite the distaste for "putting a price tag on a life," anyone who designs highways does this. They have a limited amount of money for safe design, and while there are all kinds of safety devices that can be installed, we don't simply spend every possible dollar on every conceivable device. That's essentially deciding that some level of expense to reduce accidental deaths marginally is just not worth it.)
In any event, you can simply assign a very high value to the entirety of someone's life, and deliberately wiping out any chance of them ever satisfying them would be seen as unacceptable. Doing that to millions of people would be abominable under such a system regardless of the good on the other side.
Your utility monsters will, of course, see what's on the other side as so utterly wonderful that it balances it out, though. They're monsters, after all. They'd be monsters if their reason was "Deus Vult" too, though, and we've had plenty of those.
The doctor, under utilitarianism, would actually be morally obligated to rape this woman. Take a few moments to think about that. No thinking person with any modicum of human decency can base their morality off such a disgusting, abominable system of thought that can allow for situations where rape is a moral obligation.
There are a number of ways around this. The preference to rape or murder is one that is worthy of being given no weight, so there's no paradox here as doing it could be of no possible benefit.
Further, regardless of whether the doctor would ever be caught, he would himself know what he had done and if he had any decency, his self-image would be permanently destroyed. He would know he was a rapist. Utilitarianism doesn't mean treating people as if they were mindless jackoff apes whose highest goal was momentary physical pleasure.
Finally, it's a contrived scenario that could never occur in reality, as one can never in reality be certain of the outcomes of one's actions. So who cares? That's never going to happen anyway.