I think the only thing to gain by a third party EVSE is smarts and internet integration. A lot of the newest ones connect to your home WiFi and can track how much electricity the car is using, connect directly to OhmConnect for OhmHours, Alexa integration, etc. That can be a nice feature. The only way to track electricity use with a Tesla wall charger is one of the 3rd party apps, which can sometimes cause extra battery drain.
But you gotta use your adapter daily and open your charge port manually vs with the HPWC button. So it is a trade off.