Power is needed for the full “smart toilet” experience, which can include a heated seat and warm water, and other less useful features like a self-opening toilet seat. It’s hard to go back to a regular toilet or a cold-water bidet!
The fancy ones have are built with a heated toilet seat, a water warmer, timed shutoff, and automated spray patterns. You pay a lot more money for those features, but they are nice to haves vs your basic cold water wash.
No, I live in the Rockies so my water is plenty cold. It just doesn't bother me that much. I suppose if I could make it warmer I would do that but I don't care enough to deal with putting an outlet in to warm the water.