I'm not too worried about non-Tesla vehicles overrunning Supercharger stations. With the vast majority of automobile manufacturers now adopting the NACS ecosystem in the next couple of years, it means that non-Tesla EVSE companies are going to be installing more NACS plugs. In my mind that's a win-win situation. Sure, some of those EA, EVgo, and ChargePoint stations may not have the equipment uptime as compared to Tesla, but more competition (read: availability) should mean better (more) choices.
In my admittedly sparse long distance traveling, I've only run into one time where I had to wait for a Supercharger as an owner. That was a July 4th up in Truckee, CA. There was another station a few miles away but I decided to stick it out where I was. Waited maybe 15 minutes; wasn't too bad. If you carefully read the first sentence in this paragraph, you'll notice I put in a qualification: "as an owner". Back in Feb. 2018 when I had rented a Model 3 off Turo.com, I needed to recharge the car before turning it back over to the owner. I went to the Mountain View, CA (Computer History Museum) site and queued up for over 30 minutes. There was actually a person guiding people into open stalls and making sure nobody jumped the line. Haven't seen that since....