Here is some insight from a former luxury brand service manager in the Philadelphia area. The big issue with loaners is the sense of entitlement every luxury customer has. There is a disconnect between sales(who tells every customer they can have a loaner), and service(who expects some of the people with simple quick items to wait). Everyone wants a loaner for everything, tire rotation, oil change, anything you can think of. Then you have the customer with the brand new vehicle that has the car towed in and no transportation...............flat tire, major issue, doesn't matter, that you almost have no choice but to give them a loaner. Customer decides to wait for 2 hour repair, something breaks........loaner. Also, while every repair has an estimated time not everything goes smoothly and gets done as originally estimated, some people who get a loaner for the day end up with a 3 day loaner. Finally, and this is my favorite.......most people think loaners grow on trees and its fine if they keep them for an extra day, 2 days, etc, and you literally have to track them down or threaten them to get your vehicle back. I have literally had to drive to customers houses and steal our loaner vehicles back from the customer............
And yes, this happens at every dealership I've been to. Ironically, the only dealer/s that seems to be more top of the game was Hyundai/Chevrolet that I once worked for. The difference here being that the loaners were actually run out of a dealership run rental department that was for profit with a large fleet and got paid from the manufacturers for the loaner vehicles. At almost every other dealer this is/was a mostly non profitable venture.............
I know Tesla is a different beast, but I assume they face similar issues on a daily basis......