My guess to the biggest reason not to do this is safety - if somebody is being electrocuted, you want to be able to pull the cord out of the wall as quickly as possible to maximise their chance of survival.
I just buy cheap $2 bottles of shampoo and use it for my whole body. Cheaper than shower gel, and I’ve been doing it for over 5 years with no problems. It’s all soap, right?
Exactly! Although I find dishwashing detergent dries out your skin a lot more, so I wouldn’t try using that lol. Shampoo has a pH closer to your skin than a bar of soap, so is really quite well suited for it.