You are right Roses about the difficulty of baths for elderly people. My parents, who lived in their own home until their 90s didn't have a shower and my Dad used to stand in the bath with a sponge and wash himself down there. Mum couldn't manage to step over the edge and into the bath so had a strip wash at the sink. They were both clean an practical folk who adjusted their toilette to their physical problems.
That said, I love my walk in shower and haven't had a bath since 1996 when I slipped in the bath, fell and chipped my shin bone on the taps. It took 6 months for the resulting haemotoma/ulcer to heal. Baths can be very dangerous. A friend of ours fell asleep after a little too much wine and drowned in his.