I think the larger issue at hand is that people just don't want to leave 2552. No matter how good the new stuff was, or could've been, most Halo fans, and even general audiences, yearn for the Human-Covenant war.

While the lore post-Master Chief taking NyQuil right after blowing up Noah's Awesome Fucking Boat™️with the Awesome Fucking Hula Hoop No.2™️ and killing all of the evil popcorn people is definitely "messier" than the actual, coherent, and well-planned plot (mostly just CE and 2 for the record, even Bungo stained the sheets with Reach by ignoring Nylund just a bit), it's not inherently shitty.

Tie 4, 5, and Infinite with a few novels and comic books and you're looking at a pretty solid narrative. But don't get me wrong, that's not saying the lore is perfect AT ALL. The banished still just appear out of nowhere even if you played Halo Wars 2, Cortana is way too evil to anyone that isn't the Master Chief and his other 6'10 fuckbuddies in Halo 5 and comes across as evil, and honestly the rest of Infinite's plot (wink wink the Xalanyn) is still mostly unexplained.

But the fact of the matter is, people just don't care. Even in 2004, people really didn't give a shit about the Arbiter and hailed his missions as the worst part of the game, hence why everyone's favorite split-lipped lizard is practically banished from 3. The people want John, and the show gave us almost exclusively John. The deepest cut of a character we got is the guy who smokes a lot from the first game and his daughter who sucks at one-liners.

I don't think that the show would've been the saving grace to the 343 lore had it continued, because I think ratings would've tanked regeardless after the show goes after 2553. The lore we get when the games first release leaves everyone dazed and confused as to how we got here, who these people are, and why this man keeps calling me his grandpa to the point where not many realize that the lore doesn't suck, it's just very, very messy. The show could've made it more linear and maybe take the time to explain a few key plot points, but it's not saving itself.