That indeed happens, but going by the gut isn't a bullet-proof moral philosophy. Snap judgements are something we can evaluate and consciously calibrate when we're not in the heat of the moment.
> lots of intelligent philosophers have argued against utilitarianism and have brought up flaws in utilitarianism
Yeah, I read some of those, many are really solid objections. I'm not arguing that utilitarianism is the be-all, end-all moral philosophy - just that it's a surprisingly good heuristic that can be pushed quite far before it starts to go "off the rails". And primarily, I'm arguing that working with approximations and heuristics is something we know how to do - not being able to compute a perfectly precise answer isn't a valid argument against a method.
Does it? You seem to be marginalizing across the entire population, but it's eminently obvious that most humans do _not_ see a human and erase all aspects of their being and then consider them to be one human in a uniformly distributed pool. Humans make snap judgements based on hundreds of subconscious factors all the time. Most humans look at a person and immediately bucket them into a cohort using some mix of physical attributes and prior beliefs of these attributes. Once we're in a cohort, relative probabilities can change. In this particular example, what happens if one of the 3 happens to be wearing military fatigues? What if they have a well-known authoritarian political symbol on their clothing?
Anyway, lots of intelligent philosophers have argued against utilitarianism and have brought up flaws in utilitarianism, such as Utility Monsters, and then there's the issue of even being able to impose a utility-based order between disparate things such as "tasty candy" and "rocks underneath my feet". Feel free to read those on the internet.