There isnt one (a manufacturer roadside assistance program that would pickup the car "in a flash, no questions asked" for a 7 year old out of warranty vehicle.
If this is an example of the worst customer service this OP has ever received (thread title), they have had a pretty good life. I have several examples of things that have happened to me that are much, much (much) worse than "sorry we cant pick up your car on the side of the road".
I wouldn't expect "free" service for out of warranty either.... BUT Tesla does seem to go out of their way to treat the customer terribly and try to squeeze that out-of-warranty person for every penny they think they can get.
Now contacting the manufacturer for a flat tire / damaged wheel, to me that's a bit much. I'd contact them if the problem was related to what makes a Tesla special - the battery system - but outside of that, there'd no reason to contact Tesla. Why do I say contact? Oh that's right.... BECAUSE YOU CAN'T CALL.
That's plan #1 in the "treat the customer like *sugar*" playbook. If they can't call you, then there are less customer issues (that you hear about!) That's great for the shareholders. Also one person on a keyboard can cut-and-paste answers to at least 12 separate windows at the same time, so that's less people needed to be paid on the customer service side too. Profit!
Then there's the "we can be objectively *sugar* to the customer" plan, where if they see an opportunity to screw something up during work.... Do it. Charge the customer for parts they didn't need, and the labor for those parts, and you get more profit! Oh, a window needs adjustment b/c the calibration is out? Don't tell them that THAT is the problem (or show how to fix it)... Charge them for changing out the entire window regulator unit for $400 - and then make it OBVIOUS that the work wasn't done properly by not even securing the window or making the original adjustment that was needed! (YES, this happened to me and the window worked perfectly fine, it was just out of adjustment but they charged me anyway)
OH, and the best one: If you can REALLY screw the customer and make profits over pissing them off forever so they will tell ANYONE with ears about how they have been treated.... Do it. Reach into their car remotely, and take away (software limit) the range that they have been driving around on for the months since they bought the car, and hold that range for ransom. Then when they complain face to face about theft of vehicle features - ask them with a straight face: "Don't you FEEL BAD that you have been enjoying that range for months based on Tesla's mistake, don't you feel bad that you were STEALING THAT RANGE from Tesla because you haven't paid for that battery upgrade?"
Yes - this ALSO happened to me, a 90kw pack was installed at the end of the warranty before I ever bought the car, and they didn't cripple it to 60kw (yet it is still just as heavy!) until last week - and somehow are trying to blame ME for this, while trying to extort $4500 from me to return functionality they stole from my car.
The bad PR is the only weapon we have, and in ONE WEEK I have told no less than 25 people so far about this, who were ALL horrified about how the company has treated one of their customers. That level of shock and horror will likely mean that at least a few of them will tell someone else. Until such time as this debacle has been resolved, I plan to CONTINUE being a wrecking ball to Tesla shareholder value by being brutally honest about how they have treated me, to anyone that asks what I think of the car.
My answer is and will remain: I love the car, I hate the company. If the company wants to TRY and unscrew this (since I know they read this forum) - Find the Twitter message to Elon and Tesla from Gator Audio and CONTACT ME. I'm a journalist. You REALLY don't want me this pissed off.