Edit: to further expand on this, finding the downed plane is a lot more important than it sounds. This could technically be classified as spillage considering there is classified tech in an F35. Foreign agents would benefit if they found it first. I'm pretty sure there are recon teams trained to recover downed aircraft in military zones. Considering they still are equipped with radio for communication, I'd imagine even just an encrypted message at time of impact could be useful.

Losing a plane over friendly zones shouldn't have to worry about having a beacon that's always on. I fail to understand why it would be silly to believe one could be useful in a jet fighter, stealth or not. I'd imagine it's likely even present but just defunct for whatever reason in this scenario and details can't be revealed about that, as again, it still contains classified technology.