I'm not sure even the finances would work out.
So you have an asset--your car--that let's just assume you're fine with it being something economical to drive and you don't need to keep a bunch of personal stuff in it. Now you rent it out.
So you're in the single vehicle fleet management business. Your asset depreciates mostly on a per mile basis. (Not entirely but a good first approximation.) Say 50 cents a mile cost (including fuel). EV eventually brings this down but who knows what incremental hardware will be required for autonomy.
So two possible outcomes here.
One is that reimbursement costs drop to near operating cost. Some people will want to borrow from their future selves or will figure that their costs are enough below the average to make it work. In any case, it's not a great deal for the car owner.
The other is that reimbursement costs somehow embed a nice profit for the car owner. In this case, why on earth wouldn't the sort of companies that manage car fleets today get into the business, especially given that they can do things like maintenance less expensively than an individual.