Yeah, I didn't mean to suggest that someone would do that whole 40s all in one go... maybe a handful of seconds of full-power here and there... but heat accumulates and people probably want to put the iron down well before the battery in the handle hits its thermal limits. It just seems to me like it would be a good candidate to get hot quickly and suffer in both performance and comfort due to it. I'm sure it would probably be perfectly fine for light field use.
I’d think for the vast majority of uses it’d be just fine. The duty cycle of a soldering iron is extremely low. Most of the time it’s sitting there topping up the heat on the iron, barely sipping power. If you’re truly cranking heat into some ground plane, a wireless iron is unlikely to be the correct tool for the job. Also, you could set the threshold for backing off the iron to be lower than “too hot to hold” if that’s a concern.