Money and process. They have to be certified by MS and Sony, maybe Steam. And with Bungie, at least until recently, wanting to remove content, it would be more of a hassle than creating their own in-game system. Fro example, Prestige Levi had to be replaced with a GM -- which is a joke. So rather than having to keep track of that kind of thing, my guess is they just decided to forgo it entirely.
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I never thought about the licensing part of it. I didn’t even notice the prestige achievement changed until you brought it up. Had to go check that myself. That could explain why they stopped doing it with each expansion.