I know in CT, there is a law that insurance companies can't force you to go to specific "approved" shops to get your car repaired. I wonder if the same law applies to car manufacturers trying to force the same.
I've read of one case where the insurance company insisted that any body repairs be done only at Tesla-authorized shops, and I doubt that's the only time it happened. That may be commonplace, I dunno. My understanding is that it's difficult or impossible for a non-certified shop to get Tesla to send them parts. So in that respect, it isn't possible to get any body repairs done at an independent shop unless they use salvaged parts.
Now, if you just need regular service on your car, for things like tire rotation/replacement or fluid replacement or maybe a front end alignment, there's no need to go to a Tesla certified shop. It's certainly not true that Tesla demands everybody get his Tesla car serviced at only Tesla shops, and getting them serviced elsewhere won't void the warranty -- which is another Tesla basher claim.
But if you want to take advantage of Tesla's superb level of service, their exhaustive inspections for any possible problem or even potential problem in their cars, a level of service which has earned Tesla much, much praise from Tesla owners, and is part of why Tesla cars always top
Consumer Reports' list for customer satisfaction among all auto makers... then you definitely should use only Tesla service shops.
Yes, it does cost more. As with most things, you get what you pay for.
Now, that said, it certainly is true that in some areas, there is a chronic backlog at Tesla service centers. That is an unfortunate result of Tesla growing so fast. Tesla keeps saying they are working hard to address this problem, but it persists in some areas, especially in Europe currently.
Getting body work done on Tesla cars is generally slower than getting it done on other brands, because Tesla's cars either have aluminum bodies (Model S and Model X) or extensive use of high-strength steel, the latter of which requires damaged sections to be cut out and replacements welded into place. Also, even Tesla certified body shops often have to wait longer than they ought to for Tesla to send them parts, due to Tesla's chronic parts shortage, another symptom of Tesla's rapid growth. All this means Tesla car bodies are more difficult, and yes more expensive, to repair than the average car. The expense of body repairs is the main reason why insurance on Tesla cars tends to be higher than average.
But then, the same is true for other "premium" brands such as BMW and Mercedes. Expensive cars made in lower numbers yields relatively expensive repair bills, even if they don't have aluminum bodies.