I'd like to suggest that players still have a choice to visit an NPC-owned garage for a simple repair of the bodywork. It is not uncommon for players to get wrecked in traffic because of trivial matters such as stupid driving fails or lag. This way we avoid people becoming frustrated with the fact that they have to postpone their role-play as well as rely on another player's schedule (who by the way would be doing nothing else but repairing bodyworks for impatient players).
That being said, I one hundred percent agree with your suggestion that installing modifications on your car should only be possible through proper role-play with a player-owned garage. A place where (relatively) knowledgeable and creative players can share their passion for the automobile. Because of the great amount of vehicle modifications offered to us by Rockstar, every car that is driven off the lot can be a unique role-play project. Players wouldn't only be paying for the modifications, but also for the wages of the employees. Good for the economy! Let the money circulate amongst players as much as possible.
It is also a good way to prevent every street corner from turning into an exaggerated Fast&Furious scene because modifying your car takes time and requires multiple parties to role-play.
It will also help to fuel a competitive market where player-owned businesses will have to try their hardest if they want to keep their customers.