This kind of thing would have cost me a maximum of exactly zero if it had happened here (Switzerland, but I'm guessing it's similar in the EU). Insurance is mandatory and the insurer of whoever caused the accident pays. Unless they flee the scene, but that's its own crime, so most people don't.
That said: We had two larger issues with our Model S so far, one time it had to be repaired in an Italian body shop while on holiday, but that was done in less than 48 hours. It wasn't even a Tesla service center, just one of their partners. The other issue involved the drive train, it started making whining noises after two years. They fixed that for free (new motor and drive train) and gave us a free loaner for a week.
One time it didn't recover from a software update and had to be towed -- again, a free loaner, Tesla paid for the towing and even had the vehicle brought back to our door because I was sick with a high fever and couldn't go pick it up. They usually make you pick it up.
Another time I snapped off the windshield wiper by accident because I'm an idiot, it was on our way to France. The service center in Geneva made room to fix this (had to replace the whole wiper assembly) and we were back on our trip less than 30 minutes after arriving at their shop unannounced.
So I guess it all depends on what's broken and where you are.
Disclaimer (do we need to have disclaimers for this now or is that just on Motley Fool?): I have Tesla shares and used to have Solar City shares as well, but the damn thieves switched my Solar City for Tesla at USD 290, so now I'm short 50 Dollars per share. Serious first world problems, eh?