The crux of Piketty’s argument is that the rich will just keep getting richer and richer than regular folks, but as AEI’s Andrew Biggs points out here, that assumes that these rich people just keep accumulating capital. Ordinarily, however, rich people want to spend lots of their wealth. Bill Gates, for example, built a house of some 56,000 square feet, thereby giving up a lot of his wealth to a host of people around Seattle who worked to give him the house he wanted.
Even if rich people did just keep accumulating wealth, I fail to see any harm in that, but the world isn’t like that. The wealthy spend (and also give away) much of what they earn from their investments.