Aren’t a lot of jails private and for profit? Just bill the tourist for the stay and detain until they pay in full (accruing even more debt in the meantime). It makes perfect business sense which is all that seems to matter to the US nowadays.
No, it's a small-ish minority of them. Most are government owned and run.
That said, there's a huge incentive to piss away money holding people so you can justify your budget and use poor conditions to justify increases in budget. And on top of that the contractors that supply government jails are pretty evil too.
So it's really a distinction without a difference at the end of the day, it's all a pretty rotten system.
ICE sure isn't. That is tax payer money at work, sadly.
But yes, there are incentives that do reward cells and even individuals for number of imprisonments. And no, they do not check nor punish "administrative errors".