In my city I have lived through multiple waves of this model.
The main drawback is that it requires a bit of planning: on the weekends, everybody wants a car.
I can count with one finger the companies that have survived multiple waves of this model over the last 15 years. They have "poor" cars, but enough of them, parked in "centralized" locations to ease maintainance, but enough of these locations spread out, great prices for a day, a weekend, etc.
Most other companies that tried this have ended up defaulting the moment they had to repair their first wave of cars.
The ones that still "survive" have gone through defaults, mergers, and have "infinite" amounts of money (e.g. owned by car manufacturers that use them as a way to get people "try" their cars as opposed to a "profitable" business). These are kind of "gimmicks" that you use when you pick somebody from the airport to show them around in a nice car. For everyday stuff, these are expensive enough for competing with Uber, and at that point, I just take a Uber. For one day trips they are also expensive enough that, if you take 3 days per month, owning a cheap car is actually cheaper and more practical than using these....