FWIW I agree it's frustrating when any of our vehicles are not working to our expectations, and it takes more time than we think is reasonable to get it taken care of. I have high expectations for customer service, having spent my whole career needing to deliver it to my customers, and I expect the same especially with premium brand luxury brand vehicles I own.
That having been said, I try to first consider if a problem with my vehicle impacts my ability to first get to where I need to go or stranded me on the side of the road as has happened in the past with other luxury vehicles -- for me, that has the most importance and I would consider it a "drop everything to get me going" situation. Anything else can wait some period of time. I personally don't have an expectation any dealer is going to come to my place to pick up my drivable vehicle and deliver it back -- if I did, I likely wouldn't expect that to be as quickly as when I have to take it in myself.
My Tesla is certainly the most expensive vehicle I've ever owned, but it's still not a hand-built Bentley or some other sort of specialty car where maybe my expectation would be hand management of every situation or concern I had. I do come from 20+ years of Lexus ownership, and 2 years of both BMW and MBZ. Service with these other premium brands were wildly different... Lexus was always excellent, but took a few days to get into service, and always with a loaner. BMW was problematic and could take even 10 days or more to get in when my 335i was in a crippled "limp mode" state where I could not go over 55 and was more than 3 hrs away from home. They were also not the most expedient in returning my car once they had it. MBZ also consistently took more than a week to get a service appt, and like BMW, always took another 2+ days if parts needed to be ordered from "back east" -- at least I always had a loaner from them. None of my dealers offered to pick up my vehicles. For context, I live within a 45 min drive of 5 different Lexus dealers, and similar number of BMW and MBZ dealerships here in SoCal, so I'm not out in a remote location.
I agree perhaps that the wait for Tesla may be too long and they need to increase the capacity in your area. Have you emailed customer service with your dissatisfaction on timeliness of repairs? I've read mutiple articles about Tesla Execs being focused on this, as well as have seen at least one YouTube video of an Exec making those statements while reaseaching Tesla before ordering my MS a couple months ago. Posting your dissatisfaction here helps ones soul and gets a little social media interaction, but may not get as much help as if you escalate directly within Tesla itself. In any case, as Jeff was suggesting, take a deep breath, and good luck with your repairs. My best.