If the rear wheels didn’t steer I could just reverse the rims. Since they do steer the tires with chains come too close to the frame on full left or full right turns.
The manual says to remove them when chains aren’t required. I’ve left mine in place since the tractor was new. It seems to me if they can withstand the weight of a 300 lb blade and the stress of chains slipping and grabbing on ice the weight of a mower shouldn’t do any harm.