Many people do replace the RV style outlets with residential when they fail, it does take a bit of work as you need to add a box.
Biggest issue I would see is running a new wire back to the circuit breaker panel. Then being outdoors, it really needs to be GFI protected. On top of that I do not believe the circuit breaker panel has a spare slot.
Personally, I just run a heavy duty extension cord from the pedestal to my outdoor cooking area.
I have considered installing a male outdoor outlet on the back side of my TT on the chassis, and running a new line inside my TT, to power an electric space heater in the cool months. Instead you could run a wire over to your cooking area and install an outdoor rated residential outlet.
https://www.amazon.com/Leviton-5278-...7923495&sr=8-2 This is a more expensive one listed on Amazon, but it also looks to be of better quality.