I gather it might make a difference to the selling price or the ease in selling a house in the UK, here it doesn't, so I shall not attempt to answer that.
It will, as you say, make a great deal of difference to your personal safety to have the bath removed and a shower installed that is large enough for a shower seat if desirable, and large enough for a carer or nurse to help you shower, if that should become necessary.
Here a small shower would not do in the context of anyone employed to help you, so check Health and Safety requirements where you are.
Falling in the bath, can, as I am sure you know, result in an accident that will permanently incapacite you, if you are unfortunate.
If you live alone, take into consideration that with a broken hip you wouldn't even be able to ring for help!
Tell your plumber what your requirements are and why, and don't let yourself be talked into a smaller tub and a smaller shower.
If making the alteration, have a shower with room for a carer, or a wheel-chair or even better, both at once.
A shower will also be a saving on hot water and water rates, as you will be using less water and heat to heat it.