I can't look at this as a negative against the idea, honestly. If you're rich enough to have several vehicles and you use them enough that they require maintenance often, then well, that's good. It's a money sink and a good way to re-distribute cash. If you want the convenience of owning and using several vehicles, then you should have to suffer the side-effects of such a thing. But then again the more I think about it the more RP opportunities pop up: if you're truly too busy to go get your own car fixed... why not hire an assistant to do it (I mention this to you specifically because if I remember correctly, you mostly roleplayed characters who would, realistically, be able to have such luxuries)? In fact, if you're rich and influential enough, why the hell not have your own driver - who would be taking care of such minutiae of every day life while you got on with your own roleplay? Spread your wealth - and ease your burden, more roleplay for you, the mechanic, and whoever you want to hire, and as a bonus, money trickles down from the more fortunate to the less in a natural way.
This IS a good point. We'd have to do something which I am very much not fond of in multiplayer games - trusting that supply and demand even out. This very rarely works (barely works in real life anyway) because well, it's a game and not real life. People get bored, people troll, people intentionally spite one another even if they could make more working together. It's a complicated issue and in my mind the one pure negative this idea may bring. However this could maybe be alleviated by:
Minimum service should always be guaranteed by the server. Pay-N-Spray should remain as a "bare minimum" mechanic - something that allows you to fix all visual damage (I'm not fond of the idea of every second car looking like a junker because no mechanics have logged on recently) and keep your car rolling, albeit at minimum condition, and soon requiring another visit if you drive recklessly. At the end of the day it's a game, and we have to have concessions or soon enough everyone will be riding bycicles instead (should these be influenced by the same mechanics, by the way?)
In my opinion this is one of the positives. It gives taxi drivers, personal drivers and bus drivers more reason to exist and facilitates roleplay between possibly hundreds of people. Plus, you can always have a friend take you.
On the topic of how often maintenance should be required, I do believe it should be common enough to warrant thought, but not common enough that it'd get annoying (revolutionary thought, I know). Make it take months and nobody is going to bother roleplaying a mechanic so they can do an oil change once a day, if they're lucky, for someone who will probably drive in and GTFO ASAP. I wonder if it would be possible to tie a vehicle's state to kilometers or time driven something like 15 hours driven - or something like 3000 kilometers? From what I can find online, GTA V's map is around 8km by 10km, which should hold up for around 300 turns around the map? It'd certainly take some fine tuning and I'd expect it to take a couple of months or more to reach a state where it satisfies most players in how long it takes for a vehicle to deteriorate but I definitely think it would be worth the effort. God knows LSRP needed money sinks and trickle-down mechanics (never thought I'd say that, lol).
If all else fails, encouraging mechanic roleplay as a tip for new players could help keep mechanic shops populated - and set players up for success in finding avenues of RP. Sorry for the ridiculously long-winded post, but things like these deserve a lot of thought because one mechanic can easily influence a hundred others and server balance is a precarious thing, that must be kept from the start, or it will never be there at all.