While we do have capital punishment we no longer do it by hanging.
Cheap, easy, reliable, fast, painless.
After decades of trying to build newer and better contraptions for execution, spending millions, and coming up with complex machines, routines and procedures, drug cocktails, etc. we should ask ourselves why not hang people? From botched electric chair and gas chamber executions, the mess of shooting, or the the failures of injecting, the one method that after all these years still makes more sense that any other but is simply not “sophisticated and ritualistic” enough, is hanging.
Carbon monoxide would work nicely too. Completely painless and odorless. You just fall asleep and don't ever wake up.