In theory you should be given what you need and will help and not hinder you. I agree it is easier to rest your hands using crutches because you are stationary, and the crutches are steadying you.
If you have no choice and are given crutches, keep saying how unsteady you feel and you are likely to fall. The physio will wake up when she hears the word fall!
Soon after recovering from the anaesthetic, you will get a cup of tea then goodbye! 100 years ago you stayed in until your sutures were removed. It has gone too far the other way now.
After both knee replacements, the last in 2018, I came home with a pair of crutches. It wasn't easy because I live on my own.