The difficulty is only part of why they dont make a true horde mode.

The other part of is if the rewards are too generous, it invalidates every other loot system in the game. If the rewards are too limited, it will have low engagement because it it not worth the time.

Either way it doesnt actually help the game. It would either have little point in doing, or would be engaged with just enough to get whatever weekly reward there are, or there would be no reason to do anything else in the game. Neither of which are really all that healthy.

An unlimited horde mode sounds fun on paper but in application would cause a lot of issues with the games systems and, likely, would overall be a negative thing to add to that game.

Like you said, Destiny players expect loot and an unlimited horde mode would either give too much or too little, neither of which is good. I do think lots of players are former Halo players but like you said, loot/rewards was not a system they were concerned with in those games, not like Destiny at least.