Their service centers are backed up because they don't have parts for cars, and they don't have enough service locations for the number of vehicles they've sold. Something Elon said he would personally fix back in 2018.
No, it's not a good idea to make a new owner feel abandoned. But how many stories do we need to read about Tesla delivering damaged vehicles, and then keeping someone's car for a month or more before Tesla actually gets their head out and does something about it? Here's the problem I see. They're building more factories, but no new service locations? They planned on opening 52 in 2021, and so far none of the new locations listed near me have opened.
They don't have a choice about fixing the car, it's under warranty. But OP still needs to make payments on their loan, register the vehicle, pay taxes, insurance, etc. All while not having a car to drive. And now that it's past the initial 7 day period, there's no chance OP can just return it without issue. Every single owner before 2016 saw this coming, and Tesla didn't do anything to stave it off. My sympathy is with
@ttflyer on this, not Tesla.