We usually just turn up and have a choice of three industrial connectors to plug into with no problrms. The US appears to have an ever increasing* inventory of outlets and wiring arrangements, grounding methods, etc.
It's partly due to the fact that we have multiple voltage standards: 120V single phase, 240V single phase, 120/240V single phase, 120/240/208 volt wild-leg single/three phase delta, 120/208V three-phase wye, 277/480V three-phase wye, etc.
Add to that the fact that there are several different amperages (15A, 20A, 30A, 50A, etc.) in common use, and the array of cord-and-plug configurations becomes bewildering.
Since previous standards allowed for bootleg ground (grounding through the neutral wire) in some appliances, typically kitchen ranges and clothes dryers, there are a few extras out there that are now considered obsolete.
About the only interchangeability is that 120V 20A receptacles allow you to connect a 120V 15A plug, and 240V 20A receptacles allow you to connect a 240V 15A plug. Common household wiring uses 14- and 12-gauge (American Wire Gauge) wiring, which means that both 15A and 20A circuits are available.
Could the United States switch to something more universal? Not easily. There is too much installed base to go changing things up. Look at how hard it's proving to switch the Internet from IPv4 to IPv6. Sure, we could decide to go to just 12-gauge wiring for household circuits and dump 15A circuits in new construction, but consumers would balk at the increased cost, and electricians would balk at the increased difficulty of handling heavier wire. It might also necessitate fused plugs on every cord, which so far only exist in holiday light strings.