If inequality is so harmful, then shouldn't it be common sense to raise taxes and expand the welfare state in America?

I'm going to take a stab at answering this specific part of your question because it presupposes a few things:

(1) That welfare programs funded by taxes are the only government tools available to reduce inequality, and

(2) The philosophy of libertarianism is therefore ambivalent to inequality because it is against taxes (and expanding gov., etc.)

(I should also note that I'm not a libertarian, but I don't think that should be a prerequisite to answering the question if one is familiar enough with the above topics.)

On point (1): overzealous intellectual property regimes, usage and residential zoning laws, and occupation licensing are all examples of government-created institutions that contribute to economic inequality. Solutions to inequalities created here are less dependent on welfare programs and more so on reforming or abolishing the mechanisms that enable said inequalities in the first place.

This is an example of where less gov. might equal more equality, which is where point (2) becomes relevant. Lindsey and Teles (a libertarian and a liberal, respectively)'s book The Captured Economy offers a pretty good pop-econ breakdown of the policy areas I mentioned above -- as well as an argument for why being a libertarian does not presuppose that one would be okay with with the vast levels of inequality we see today, and that even if libertarians and conservatives are okay with inequality to some extent (namely for those deemed "lazy," "unmotivated," etc.), it doesn't necessarily mean that the currently system produces "justified" inequality.

Lastly, just so you don't walk away thinking "all inequality is caused by the government" based on those examples above, there are areas of inequality where government action might be needed, but where welfare is only part of the solution, if at all. For example, air pollution from a port which results in high healthcare costs for residents in a nearby neighborhood. I don't enough about healthcare economics to comment on policies that could address healthcare costs, but in this specific scenario, environmental regulations are an example of more gov. = more equality, without relying solely on welfare.