It's an extremely complex and interesting subject. In France, the debate on taxation and wealth inequality is also a hot topic (the kind of thing you avoid talking about at the dinner table). France, with its progressive tax system, is trying to reduce income inequality, but the challenge remains to strike a balance between fair taxation and promoting economic growth.
The idea of a single tax rate has been discussed, but opinions are divided. On the one hand, it could simplify the tax system, but on the other, it could also lead to an increase in the tax burden for lower incomes and a reduction for higher incomes... Thus, increasing inequality. And I agree.
But yes, this challenge goes beyond the question of taxation, and it's really hard to think about.
If the income tax was a flat rate, so people can earn whatever and pay the same, but there were higher taxes on investments, it would mean that the richer who can invest, will still make gains, but not as much. The incentive should be there to work and add value in some way to society, not just make money.
In fact, it's crucial to strike a balance that doesn't penalize the lowest incomes. I'm very bad at economics (not small-scale economics, but big economics like a country's), so it's hard for me to go any further here. That said, applying higher taxes on investments for the wealthiest seems like a viable solution.