I think one depressing example is innovation in weapons and other dangerous fields. "If we don't build it, someone else will first" is unfortunately historically been shown to be true, has it not?
Today's unsavory borderline reactionary doomposting brought to you by: my crippling fear that I'm isolating myself in a political echo-chamber (so naturally I gotta hop online and exclusively ask my fellow leftists)
Yeah that's not true at all. Markets are just a medium of exchange, and they can be used under for profit or non-profit systems. For instance, coop housing exists on a market and would continue to even if all housing became coop housing.