You have a fundamentally flawed view of what wealth is. Well isn't a thing. It's not like there's a limited amount of wealthonium in the world and whoever holds it gets it and nobody else does. That's not how it works.
Wealth is created through activity. Without the activity there is no wealth. Therefore the supply of wealth is endless, the problems usually come with limits or issues with the activity
So no, increasing wealth inequity is not the issue. The issue is that people are struggling harder and harder to be able to do enough activity that's worth enough value to be able to get what they want. That's true whether there are wealthy people or not
So the underlying issue is that the middle class and poor class aren't able to create enough wealth to meet their needs and that has nothing to do with the wealthy. You don't address that by worrying about what the wealthier doing, you address that by creating more opportunity for the middle class and the poor. And funny enough to do that you need the help of the wealthy which they are more than happy to give if they feel that it will be successful
Right now the tax burden and other burdens on the middle class prevent any disposable income or time that would allow for them to increase the value of their skills or begin to acquire assets and that is the problem. The wealthy are not excited about starting new businesses or educational opportunities that would fix this because they see the country as failing
And no reactionary politics does not follow from financial systems in the slightest.