The private sector is not a fast mover in infrastructure. It's the prototype public good, where the gains are vastly redistributed to society rather than being easy to isolate into a transaction. A road not only reduces your travel time from point A to B, a service worth $C to you. But also enables economic activity along it's path, makes it possible for you to get a job in B in the first place, etc. and all these are worth a large multiple (N * $C) for which nobody can be charged.

The net effect is that there is drastic under-investment from the private sector compared to the needs or the economic potential of a society with good infrastructure.

Generally cities prevent people from building infrastructure willy nilly. Buldozing houses or seizing public land for a new highway isn’t something that companies are allowed to do... I’d posit for good reason.

Typically P3 agreements are initiated by government and promised revenue exclusivity is the incentive to build.