Perhaps other parts of the world have privately operated roads, but I’m not aware of them.
Since you live in the area, and are talking about toll roads, I assume you also probably know of the name Cintra, who are Spainiards. And Cintra is, in fact, a private toll road operator who has owned roads around Austin previously
I mentioned Texas 130, which was operated by Cintra, but was still technically operating under TxDOT: https://en.wikipedia.org/wiki/Texas_State_Highway_130
Agree that it's a more accurate metaphor than just "toll roads".
My understanding is that Cintra exited the Austin TX toll road business around a decade ago after profits from SH 130 failed to materialize
So, the ones in states that can't afford to build or maintain them are often private roads or PPP.