Take a close look at that adapter in the Tesla store page. Notice anything funny about it? Look at the raised plastic part that has the Tesla logo molded into it versus how the metal pins in the end are oriented. That raised plastic part is on the "top" of the UMC plug, and the cable hangs down at a right angle from that. The pins are rotated a quarter turn from the "top" of the adapater. Like with 5-15 and 5-20 outlets, the round ground pin of a 6-15 would be on top or bottom, depending on whether the 6-15 outlet was installed upside down or not. But with the adapter pins turned that way, the cable would always hang sideways on one side or the other, guaranteeing strain on the pins/cable. That seems like a mistake in the design.
- - - Updated - - -
Many people, including me, have them in their garages. [...] Mine's a locking 6-20 receptacle...
So you actually don’t have a 6-15. You have an L6-15.
The 6-15 does seem like a really really obscure one. However, I did actually make an adapter cable from a 6-15 plug to a 14-50 receptacle for a weird application. I bought a Quick220 box, that can combine two 120V outlets into a 240V one. I wanted to keep compatibility to be able to plug into more types of outlets in an emergency, so I went with the 5-15 plugs on the ends, rather than the 5-20 plugs, where you could only use it on 20 amp outlets. Since that box was for 5-15 outlets, it keeps that current rating for its output, so it's a 6-15 outlet. I had never seen that used anywhere, and I wanted to be able to use it with my 30 foot RV extension cord (14-50), so I built a short adapter cable. I tested it at 11A to not pull too much current, and it works fine. In hindsight, I probably could have built the adapter to get it onto a 12 gauge regular extension cord, since the current would be less than 15A, but my initial thought was that this is already slow enough charging, so I want to not have any voltage drop and 240V should probably be on a beefy cord.