Guess I could research it myself, but just in case you know---who ran the ports before the Brits?
We really should be clearer about terminology. All ports are "run" by a local Port Authority. (Security is separate - it's the responsibility of the Coast Guard).
Some ports are small enough so that the Port Authority can manage all operations. The larger ports subcontract some operations - both for efficiency and cost.
Each Port Authority decided individually when to subcontract container management. There isn't just one Fed'l agency to manage all of the ports, but I think it's DoT that oversees the regs. for port operations. They don't dictate what the Port Authorities can do, they just monitor.