"Distributing" doesn't require "evenly". Amazon has distribution centres, they don't send stuff to all customers equally regardless of what is ordered.
The entire foundational assumption of (Smith's) capitalism is the idea that people who are better at making a profit are exactly who should be given more money to work with, and that this benefits all of society — and while I will agree that the phrase "trickle down economics" doesn't fit reality of the behaviour of billionaires (who act more like aristocrats), that's where that phrase comes from, and it seems to often work up to deca-millionaires at least.
The flaw with this (even in the case of millionaires) is it presumes no parasites. As it happens, both Smith and Marx noticed this, but as history shows, the proponents extolling the virtues of each were not very effective at preventing economic parasites.
If I read an article that titled "this NGO is distributing food and medical aid to the refugees of the conflict" and then on the body of the article I find out that a single guy got all the supplies and the rest got nothing, I would consider the title very misleading.
But the distribution for wealth under capitalism isn't "one" person, and capitalism wouldn't work if it was, because nobody else could buy anything with the money, and therefore everyone else would invent a new currency or barter, and then all the money which that one person has would be worthless.
