Did some more thinking on this while going to an auto parts store.

To me, the main problem is lack of a large enough area next to the tub that can be sat on while transitioning in and out of the tub. This can be the safety zone that allows the person to get stable before getting in/out of the tub.

After getting back home I did some more research and found there have been numerous studies done on how to design/modify bathrooms that allow more independence as a person gets older. The biggest problem is that we start to lose muscle and balance as we get older. I've quit doing my own roofing work and don't like ladders any more.

It seems there is very little that can make a significant improvement except for the accessibility.

I believe the studies show one of the best features is a shower with a flat entry.

Another was a sitting place while using the tub or shower plus using a shower type wand for bathing.

For my wife I'd try to make a seating area at either end or beside the tub for safer entry and exit. Try to make it cushioned and have the cushion firmly attached, maybe with snaps/velcro, to reduce chance of slipping. This could also be used to make it safer to undress and dress. A tub with a door could also benefit from a seating area next to the tub. A washable pillow and interior tub mat could be used to make sitting in the tub more comfortable.

Personally I don't think there would be much gained by installing a tub with a door.

My biggest complaint about using a tub to bathe is how quickly the water cools off. I don't think there is a safe method that can keep the water hot, for a normal tub, except for having insulation beneath the interior surface of the tub.