>* If a company controlled by PE goes bankrupt, shareholders (PE) likely make a profit

That's not necessarily a bad thing, or sign of anything sinister. If a business is failing, and you buy it for pennies on the dollar, and despite your best efforts it still goes under, so you liquidate it, you can still turn a profit if the price you paid is lower than what you got from liquidating it. That's not bad, because private equity (or anyone else, for that matter) isn't expected to operate as a charity. The only reason they're willing to stump up the cash to buy the business in the first place is the expectation that they'll make money. It's also not bad for the original owners either, because the fact that they hold to PE rather than someone else, or liquidating it, suggests that the PE offered a better deal than either.

>But if a publicly listed company goes bankrupt, shareholders lose their money

Often times yes, but sometimes not, eg. hertz.

> despite your best efforts

Citation needed.