Governments predate capitalism. They don't predate wealth inequality. Part of the purpose of the original formation of governments was to tackle wealth inequality in a feudal system.
One of the things that stops people at the lower end from innovating and forming for example small businesses is lack of resources. Redistributing wealth would allow mean more resources available to wider range of people. I'm sure improving bureaucratic processes for small business startups is also great thing to do.
I have a PhD in particle physics and I think that cold fusion is basically completely unviable in any situation. I may be proven wrong. I agree that taxation is a complex problem to solve, which is why I was advocating allocating more resources to this earlier on. 'Rich people who have far more resources than they have any need for and live wildly extravagant lifestyles don't need to redistribute any of their wealth because one day we'll crack a high yield problem and everyone will be able to be wealthy' is a very dangerous viewpoint as far as I'm concerned. It's clear that the current stable climatic state that our planet sits in is becoming strained by human economic activity, and the capitalist promise of 'there will always be more' is becoming more complex to fulfill. There is a clear solution which exists now, and it is to redistribute wealth.
I don't think we'll likely to come to any kind of agreement about these topics so I'm going to leave this conversation here.