Gnostic: What makes turn base mecha games unique?
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From a ludological historical perspective the interesting element was the thematic incorporation of heat as an action limiting factor. Modern warfare is very instantaneous, compare air combat with missiles at range from WW1 and WW2 dogfights. Batlletech might have been the first wargame system (in the sense you used the term) where the action point limitations made sense. These constraints both simplified systems and broadened the strategic depth (by making each decision more meaningful in itself rather than having meaning emerge as average of many decisions). Everything you do costs heat, so there is no instantaneous "I win" button, it's a naturally compensating system - the bigger and more powerful you are, the more heat you generate. Usually the tradeoff is between firepower and mobility of course, but that's precisely what modern technology breaks.
I could make a case for leadership systems being functionally similar and originated earlier, yet those always fell in some uncanny valley I think. Likely because of their origin in the period when complexity for the sake of complexity (rather for hyper simulationist goals) was all the rage. And now I think of it they are opposed to each other, leadership systems are usually a positive feedback loop, rather than a negative one. Better leader = more power (less ludological constraint), whereas better mech = more heat (more constraint). Hmmm and better leader is similar to the more experience loop in RPG's as well... whatever, I could go on for hours I think.
Theme is key also in how the sci fi setting was merged with an almost feudal setting. I'm actually quite sure that was intentional design as the parallels with medieval armored knights are very very apparent. And it worked since it made the setting very familiar and easy to jump in. Anyway those aspects to me were the meat that lead to Battletech's cult like status, on top of the giant robot bones.