I like the idea, but also think it should maybe not be available to enormous characters.
Also, have you ever considered making the game override barely mobile player characters' trips out? Like how sometimes asking a barely mobile girl out would have her ask you to come to her place instead?
That makes sense; if a character is fat enough to need a care home, they are probably past the point of using mobility scooters to travel into town.
Overriding the player's decision at barely mobile could provide another advantage to owning a scooter or high fitness, as both of these could allow the player to overcome it. I'd like to introduce player Dizzy's addiction, which might work similarly - the player would have to pass a roll check to see if they can do what they want to do.