Note that the comment you replied to didn't mention distributing things equally. Just noted that allocation is the problem that needs to be solved.

Not speaking to you in particular, but many people seem to equate any talk of redistribution to the extreme case of absolute equal distribution. But I've never seen anyone rationally arguing for that case. In reality, what most people seem to want involve some concept of 'fairness' in deciding who gets what, or minimums to what people should get just for being a part of society, or perhaps sane limits to the deviations between bottom, middle, and top.

So, yes, the questions you ask are exactly the questions we need to solve. How do we decide who gets the best surgeon, and who gets the trainee? How do we decide who gets a mansion with a view and who gets a closet with thin walls, if that? Most people seem to think that the way we are doing it now isn't ideal, so what is ideal, and how would we get there?

Your questions are unresolvable, because the person who gets the worst heart surgeon is inevitably going to agitate that the system is inequitable and unfair.

It isn't solvable in a binary way, certainly, but we can potentially find an optimal solution that at least reaches a level of fairness that the vast majority of people are comfortable with. Yes, you're always going to end up with some people unhappy with their lot, but there's a huge gray area between not pleasing everyone and not pleasing anyone (aside from a very few very lucky people).

If the most benefit for the most people is your criteria, historically a free market coupled with enforcement of basic rights has done the best.