Can you hook up Canon speedlight to a wall outlet?

It's Happy Trigger Finger that causes the damage!  The power supply, whether it's Canon's battery tray, Godox, Quantum or Tronics Speedfire, only gives you the capability for quicker recycle. It is the photographer getting carried away.  Read page 7 of the Canon manual for the 580EX. It says not to shoot more that 20 flashes in a brief period of time, then give the flash 10 minutes to rest.