It's the 21st century. Heating water is something we worked out how to do before we invented the wheel.
You're missing two of the main issues here. Some of the cubicles are too narrow (see Forbidden Valley toilets)
you have forgotten kicking cubicle doors, throwing wet loo roll over the cubicle sides. I do feel sorry for the cleaners when they have people go into the loo's that don't give a damn and mess around.and too many people think it's a playground and feel the need to shout and make noise in them.
mmmmmmmIt's the toilets with the sloping roof and Velux Windows within them that I find bizarre - during dark nights such as Scarefest and Fireworks the windows turn into mirrors and everyone can see you doing your business!