I've had no problems with my Mobile Connector (although I've only used it a few times, since I use a Clipper Creek EVSE at home), but most Superchargers don't work for me. In fact, a Supercharger stop on a recent road trip was the first time (of half a dozen or more attempts) that a Supercharger has worked to open the charging flap for me.
For me, it's no great hardship; I just tap the charging flap with my hand and it opens; or I use the screen before getting out of the car (although then, if I close the car's door, the flap closes so quickly that I might not have time to plug in before that happens). Tapping the flap is an approved way of opening the flap -- it's mentioned in the manual, with no caveats or warnings against doing it this way on a regular basis. Note that owners, like me, who have J1772 EVSEs don't have the option of using the button on the EVSE's car-side plug to open the flap; we must rely on another method to open the charge port flap.
Presumably the button on the charge handle sends out a short-range radio signal that the car receives. My hypothesis is that my car's receiver is barely sensitive enough to detect a signal that's even slightly weaker than intended, and that many Superchargers' signals are weak enough to be iffy for my car. Presumably swapping out a component in the car would fix the problem, but it's not enough of an issue for me to call for service. I might mention it when I take my car in for routine service, though.