Risk neutrality will definitely lead people to greater wealth on average, but it will also lead a larger number of people into ruin, since that's the point of risk aversion. So, we do expect rich people to be more risk neutral, because that's how you get there.
I'm not sure what the evidence looks like wrt wealth influencing a person's risk aversion. In economic models things like risk aversion and time preference are assumed to be immutable in an individual. However, that assumption is known to be sort of dumb and is generally made so that the models are tractable.
There's a bunch of interesting work in being able to manipulate risk tolerance on different timescales; which is an instance of key aspects of a person's life-strategies being "configured" by early exposure to environmental features. A nice account is this book, although there are some controversies.
(In healthcare, the lingo is ACEs -- adverse childhood events. It's foundationally the same evpsych ideas, though the healthcare people are too solipsistic to connect to the larger science, as per usual.)
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IIRC the essay splits risk tolerance into relative and absolute risk. It argues that even if someone poor has the same risk tolerance as a rich person relative to their wealth, the poor person's absolute risk is lower than the rich person's. When iterated on in the simulation they provide, the difference in absolute risk tolerance causes a very large wealth gap.
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