I had a headset with that feature, and sure enough, it failed me on a sales call. I groaned at something our salesperson said, and despite the button having been pressed and the light being on, everyone heard me.
And yes, there are many ways to avoid this problem. I think adding a resistor and capacitor to form a high-pass filter for the shorting option would work fine. If there is already a PCB for the switch, adding these two components would cost practically nothing.
XLR switches are easier, just short hot and cold, done. Works with all microphones and doesn't produce a pop, because XLR uses phantom power instead of T-power.
There is a microswitch in the mic boom, so that it is disconnected when you lift it away. I mean, you can't get more simple: when it is in front of your mouth, it is on, when it isn't, it is off. No need for a LED. Also, the headset is passive, with a good old jack connector, I consider it a plus.
Got a wired Plantronics headset with USB-C that I'm happy with. Not sure if the above products have this feature, but I recommend checking for it.