If entrepreneurship is the solution to society's ills why don't entrepreneurs solve societal problems? (note this criticism is equally effective when pointed at non-profits)

If there were profit in it, they would.

Society's ills tend to concentrate around people with no money or resources. There's no profit to be had solving their problems, so entrepreneurs are not interested.

Non-profits on the other hand, depend on the existince of the problem to justify their own existence. So they are not well-motivated to solve those problems, quite the opposite in fact.