I dont think that is going to happen because rich people have better investments where they can invest their money than bitcoin. They are going to have the power but the price would go up very slowly because they would own 90% of bitcoins.

Maybe if a few billionaires decide to invest hundreds of millions of dollars( this looks like a big amount for us but for them it is not that huge) into bitcoin that will change the situation. But that is less likely to happen because bitcoin is not the best place to invest that huge amount of money because if they control 90% of bitcoins the price will go up very slowly or it will maintain.