Slavery is profitable. People only stopped doing it when it was perceived as immoral.

Lots of things are profitable but immoral. People will do crazy immoral and illegal stuff for money, but we outlaw and slander the more abusive stuff, like monopolies and such.

If it wasn't pensions that were funding PE, I'm sure PEs would get a lot more criticism and would not be allowed to do what they do.

Misconception, slavery is not profitable if you do it in your own country with a massive base because those people aren't economically active and don't buy much with their non existing money. In fact many historians argue slavery ended due to capitalism, not morals.

Yes you can pick up cotton at a lower labor cost with slaves, but you can't charge the slaves rent, sell them useless clothes, tax them, etc.

The idea that slavery is a free lunch that is only banned on moral grounds is wrong.

Slavery is bad economics. If you want your economy to grow, paying workers is not bad. Economic growth isn't zero sum.