What usually fries first is the step-up transformer or some passive crossover component.There are lots of stories here on the board about "painful" audio, etc., but I've never read about "fried panels" or the like... is that because we're all too civilized to mention anything like that?
The 'painful audio' is likely caused by amp distorting and room ringing. I have tons of power (1,200w into 2 Ohms), so don't ever hit amp distortion, but it's easy to make the room ring. Or at least it used to be before a literal ton of room treatments.
An ESL transducer alone is pretty robust and can take abuse, as long as there is no arcing.