After all, your prosthetic foot won't care if it steps in a mud puddle or on a bumble bee. It is plastic of some sort. It's shoe like....
All I can say is I have seen what it looks like to have one shoe on and one prosthetic foot unshod. It is startling. Shocking. Actually, it freaked me out for a second. I'd just watched this older fellow jump out of his truck, and thought it was weird that he was wearing two different colored shoes. Then the realization that I was looking at molded toes on the peachy colored shoe.
I just think the answer is yes. Yes, you really do need to wear a shoe in shoe appropriate settings. Such as a rainy day in the Puget Sound when you are walking in a parking lot.
Let's just say, No Shoes, No Shirt, No Service applies to everyone.