Charlotte has been having caths by herself since she was about 15 months or so.
I started intially as we were living in a VERY small unit, with no bath, so she would sit in the TINY baby bath we had from when she was a NB in the bottom of the 'roman bath' (shower lol). The bathroom was in the middle of the house, I would put towels ont he tiles around her bath and on the floor so she wouldnt slip over if she did get out and used to do the dishes and keep an eye on her.

However, Charlotte has NEVER been a stnad up in the bath type - has always been aware not to do that, she doesn;t touch the taps at all ever, again she was taught from the beginning tht only mummy and daddy touch the taps.
Now we live in our own house with a propper bath, she still baths alone if she wants to (she more oofen than not kicks me out lol) but we can see her from the couch or even the patio if we need to. And she doesnt get herself in or out of the normal bath as she did with her baby bath in the shower set up. lol She is really good in the bath, and I trust that should something terrible happen, it would be/have been a very isolated and unpredictable occurence - she is always within earshot, and always within 30 seconds travel time from anywhere in the house.
So I think it really does depend on the child and how they are known to behave and respond to instructions