The profit in infrastructure is economic growth and optimizations of people's mobility. This can only be done by a state. A state can still mess it up but it is the only entity that can do it.
Good luck getting a "Taktfahrplan" working if you have to rely on private rail companies optimizing for every last dollar and having the locomotives catch fire blocking lines for hours. When the Fung Wah Bus breaks down for the 10th time on the way to NY it doesn't block all traffic but with rail you don't have the luxury to drive around it.
The extensive damage in the Swiss Gotthard Base Tunnel was caused by a bad wheel from a foreign rail company that cut costs to a point of running rail cars with wheels that have way too many km on them.