Awwww. You NEVER get to play with them...? I gotta think wandering around on my desk is less stressful than dodging birds and other yucky buggers.
Ah, well. To each, his own. I think I'd move on if I didn't get to play with them at least a little...
One note on feeding other mantids: Don't do it if the specimen is sick. I'll leave it to the pros to know the risks, but it doesn't seem worth it.
As you say, to each his own, but have you ever seen a mantis successfully run away from a bird?
Actually, though, the causes of stress in insects are quite different. A good working definition is "the response of an organism to meet all adaptive demands made from the environment." As with homeotherms like us, the reaction to stress is usually mediated by hormones, most famously in our case, adrenalin.
Insects in the wild are constantly exposed to stress and manage to survive and reproduce effectively. The question then becomes one of whether the captive raised mantis is more stressed than its wild cousin and whether that stress causes adverse physiological effects. A comparison between the problems experienced by pet mantises, sudden death, mismolts and cannibalism during copulation, and those by captive raised mantids in research labs, suggests that the latter do much better than the former.
Because of the size of the enclosures, spraying lab mantids once a day does not cause the evaporative effect found in deli cups that drops their temp by at least five degrees in seconds (I have measured this). Instead they live in a humidified environment which more closely imitates natural conditions., Also they are not handled beyond the need to care for them or teased to make a threat display. The success that we do have demonstrates that mantids can survive quite a bit of stress, but some of the ailments that they are heir to, particularly mismolts which greatly exceed those in nature or professional setups, suggest that they could do better with less stress.
I would agree, though, that the sudden appearance of a yucky bugger would be very stressful indeed. I imagine that it would scare the feces right out of the little guy.