Income equality is not a problem as such. It's a natural consequence of technology seeping more and more into society. In Shakespearean times all musicians made money by performing. The best ones performed for the king and made more money but all made money. With digital distribution, the best ones can reach everyone, and everyone wants to listen to only the best ones, so the best ones make a killing and other musicians turn into starving artists. There is going to have to be a transition of people into professions that aren't easily distributable or automatable. You don't need a startup to fix this. This is precisely what capitalism is good at doing, though it does take time, creates winners and losers and causes some segments of society a lot of short term pain.
The big problem is that if you take into account all capital invested in the financial industry, so investments in VCs, hedge funds, mutual funds but also deposits in banks, financial firms have been a) generating lower rates of return and b) passing a smaller percentage of those returns to investors. Banks in the US keep/spend 60-70% of returns generated on all capital invested with them. In Europe it's actually worse, about 90%. Couple this with the fact that the middle class doesn't have access to and doesn't know how to do due diligence on investments that generate higher returns (the better hedge funds and VCs) and that policy makers have held rates extremely low for a very long time, and you have we are now.
Even though people are not making a lot less from employment, their total income (including returns on saved and invested capital) and net worth is MUCH lower on a relative basis and it's clear that their children are likely going to be worse off than them and they may not have a retirement. This in my opinion is likely the cause of the appeal of Trump.
Both problems a) and b) mentioned above are not because the financial industry is evil. It's because large parts of the industry, particularly the parts that serve retail investors and depositors are obsolete in how they are structured, for example the very idea of a mutual fund (including ETF) or indeed any vehicle that pools capital, except in situations where material capacity constraints exist, is obsolete because unlike in the 1950s where pooling capital reduced transactions costs, it now dramatically increases transactions costs and hence lowers returns.
The industry won't fix it itself because the best and most innovative people working in areas serving retail get pulled into areas that can charge 2 and 20 and because doing so means they compete with their own most profitable businesses. Most extant fintechs won't fix this because putting an API or web-page in front of extant products doesn't solve the underlying problems.
I don't think the typical VC funded startup will fix this because there is an extreme focus on going to market immediately and then iterating. If that's your approach you are going to end up building a web front end to Vanguard or an API to ACH and focus on marketing. Decent returns to VCs but you don't actually fix anything or approach anywhere near the returns possible with a higher risk approach. Extreme immediate focus on iterating is great if you are a 20 year old who hasn't built anything yet. I don't think it works all that well if you have a couple decades of industry experience, know what to build because you are likely your own most finicky customer.
Full disclosure, I am working on fixing this. We (at different firms) built systems that essentially took the US equity market electronic and early HFT systems. That in some ways was a much simpler problem but it still took us 2 years of building and testing with our then employer's capital, essentially serving as our own clients, before we went to our first external customer. We are following the same process now, essentially coming up with a different way of structuring our client's relationship to us, dealing with the regulatory headaches that come from that, and developing novel algorithms to handle investing for retail clients. If you are interested in this sort of thing, can program well, love data science but understand that even when doing something exciting you will spend 70-80% of your time munging data, get in touch.