The issues that Piketty raises are not the result of capitalism, they are the result of democracy. The problem with democracy is that a person is very unlikely to be interested in an issue which will be to their detriment in some small fashion, while they will be very invested in ideas that will benefit them a great deal. That is, I am unwilling to spend an hour educating myself to save 19 cents a year in taxes, but I will unwaveringly push for laws that will tax others at 19 cents a year to pay myself $5 million each year.
The problem of wealth inequality arises when a few dedicated individuals make it their goal to see to it that a great deal of money is paid their way, at another's expense. In a free market without taxation, this becomes an impossibility while the laws protect individuals from such theft. In a democracy, it is inevitable that it should happen because the laws will be created only to benefit a few at the expense of others.
The rising inequality is a non-issue, given that real purchasing power has risen across the board regardless. To suggest that reducing real purchasing power across the board, in the name of equality, is a sound economic endeavor is naive.