Also, renting a space during a trip was something people were already doing. People were already paying money to stay in a strange place, like a hotel.
As far as I know, the vast majority of people don't currently rent clothing of any kind on a regular basis.
People's comfort level is going to be lowest the more invasive a product is and clothing is probably an order of magnitude more invasive than a living space. But, as you said, maybe this becomes the next airbnb. I doubt it, but maybe.
I've seen my wife share clothes with her best friend in the last week. (They have similar size/tastes and frequently shop together.)
If they already know each other and are friends, why would they need another entity in the trade?