Hello Felipe. Taxing capital income is a very sensitive topic. On one side, some people will agree that the most important lesson of the neoclassical model is not to tax capital income as it discourages new investment and, therefore, economic activity. On the other side, rich people are the ones who have the capital income, then, is a good way to tax for redistribution. Personally, I am against taxing capital income as I do not believe it tackles the inequality problem by the root. Also, it will leave an economy worse off.
In the first place, increasing the capital income tax will only make a crowding out of capital investment in the country as relative prices become higher. This will only make a loss in jobs, market dynamism and possibly in the longterm, less tax collection. Ireland is a good example of how a reduction of taxes to capital income made the economy thrive.
Second. More important than to increase taxes is how to spend the money collected. In fact, while social welfare programs help to get some people out of poverty, this is only while they actually receive the benefit. I mean, most social welfare programs fail at creating the right incentives to get people out of poverty after they stopped receiving the social benefit.
In my opinion, total income inequality creates other forms of inequalities. For example, rich people will send their sons to the bests schools, increasing their opportunities to be accepted into a good college and, ultimately, taking the bests jobs. It is a cycle. We can call this educational inequality. Another example, rich people do not have family issues related to money, but poor people do have them, affecting the child developing. I am sure you can imagine many more cases of inequalities which derive for the total income inequality.
Finally, my proposal is to create a society where all people have the same opportunities since birth. A society similar to those Nordic countries -which their capital tax is relatively low- where no matter your social status, childs go to same the schools and mother give births at the same hospitals. I believe this model tackles the two points aforementioned.