Basically, a large operation could have economies of scale (in house mechanics, only two models of car to choose from, own the fuel stations...) but the utilization of the vehicles probably would not change dramatically from the utilization of the private "fleet" we have today.
there are a lot of reasons, but here are the two big ones. unlike any rental car I've seen at an avis lot, my car is actually fun to drive. you'll never see a car with a manual transmission for rent in america, unless you go on turo. second, I take much better care of my car than most people. after seeing how people treat vehicles they actually own, I don't want to rent a vehicle that hasn't been thoroughly cleaned and inspected after the previous driver.