The unfortunate reality of PE is that regardless of your opinion of them, your money is probably tied to them.
And thanks to the current administration you will soon be able to direct 401k money to them.
It's hardly "backdoor" when pension funds and other institutions could always have bought private companies. If anything the recent shift to ETFs and passive investing is a move in the opposite direction. In the past such institutions would have managed their portfolios in-house, ie. private equity.