It seems doubtful. Extremely wealthy people have a very poor track record for solving societal problems, and a very good track record of perpetuating problems that lead to them increasing their power.
Your comment is very low on substance. Care to elaborate what kind of problems billionaires will solve, that are otherwise unsolvable?
The number of billionaire is growing and growing, and so are the fundamental problems that might be leading the world to collapse. How many more billionaires would you reckon do we need?
Perhaps my naїvety lies in the fact that I put this problem in the topic of the problems of the next decade, when in fact it seems to be the topic of the next century, where their competitor will be AI. But this can be solved very quickly if at least one country establishes a tax formula whereby the richer a person is, the more taxes will be paid on every dollar earned, without any exceptions for the richest. Ukraine might be that country if it ends its war not very destroyed.
A definition of "problem" bond to some actor. Here is the definition from Google with my notices: a matter or situation regarded as unwelcome (for whom?) or harmful (for whom?) and needing (for whom?) to be dealt with and overcome.
So, what kind of society/environment problems are they solving right now? Except of Bill Gates and pre-Twitter version of Elon Musk.