Now that is some interesting theory we've go here!
Considering that the P3 system would accept and function (as in work to some operational level) with an Inspire FW in the first place - I don't know about that but my guess it is indeed possible - then it is also possible that a FW from a different AC could cause a failure in propulsion originated in the battery system somehow.
In plain words, the FW could overload the maximum discharging capacity of the battery (commonly referred to as "C rating"), causing s shutdown or sudden voltage drop (or any other issue) in the battery or the smart management, or even in any of the subsequent systems such as ESCs, motors, etc.
That would most likely occur during a burst or other heavy demand maneuver (by command or otherwise) when the max load can be exceeded, and I'd guess it's even possible that a problem in the very P3 firmware could cause that as well in some very specific situations. Although I admit that DJI's engineering in both HW and FW are quite advanced, and most certainly operating within strict and rather safe margins. And... not discounting that we pilots can screw up this rather sophisticated system in so many ways as well, of course...
I'll check the specs of both P3 and Inspire batteries for C ratings and see about that. Tomorrow, because now I'll go out and do some flying and shooting around town - it's such a clear, warm and spectacular night here!
