High current socket failures are unfortunately fairly common leading to melting (or worse) of the socket, plug or connecting wires.
The key here is "quality". I don't know if this is a high quality Hubbell socket (and even if it is, it may not be wired properly) so I think it's wise to replace it with a direct connection to a wall charger.
Proper tt30 are all designed for frequent use since they were for rv use. They do wear out (such as in old rv parks) but it takes several years or more of daily use. Newer rv parks have both tt30 and 14-50, again for nearly daily plug/unplug.
In the op, maybe twice a week charging will not be a problem at all.
In my case, I know my outlet is quality and the wiring is more than enough, yet I still limit to 16a (120v) since that gets me a full charge in less than two sets of off peak hours. I have tested at the full 24a (120v) and no overheating at all, even if I include my rv extension cord.
An rv which uses tt30 will OFTEN draw the full 24a since an ac and microwave will get close enough so forgetting and turning on a hair dryer or the house batt charger will trip. (So many of us rv’ers are really good at energy monitoring).
While I discourage others, I built the circuit, and know my car and rv draws so well, I can run them off a splitter if I ever needed to. The side bene is I can, if ever needed, charge the Tesla from the rv generator, since the gen has a tt30 outlet. Redundancy abounds in our case.
Why did I not go 14-50? Not enough amps left after hot tub, swim spa, ac, etc. I can if needed, with extension to the oven, but we don’t commute so we never need a fast charge at home, and we have 3 SC’s within 10 minutes if we need them.