[MiroF]

> The low income might get better/more healthcare

It was a pedantic point - but taxing the rich intrinsically reduces the inequality of the post-tax income distribution because the difference between the top and the bottom is less.

> The low income might get better/more healthcare, but they don't get any more income from that spending

Lots of reasons - one is expenditures on healthcare by the employer, another is lost income due to injury/illness that preventative care could have prevented and that's before you start looking at medical expenses.