Time for a bad analogy!
This is like a dad who spends all his time at work and whenever the kids see him he's got gifts or ice cream. Mom is home all day and makes me do chores and enforces my curfew and says "that's enough Destiny sweetheart, turn it off before you show up in the news like those GTA kids". Dad is the good guy, mom is the witch.
Luke is really cool but nobody tags him when they post "BUNGIE FIX YOUR FUCKING GAME" or "FUCK YOU CROTA IS BULLSHIT" etc. Deej has an extremely annoying and roundabout way of giving us answers we don't like, but these aren't his answers. He's the proverbial messenger people keep virtual-killing.
I mean I'd be happier with a Luke-type personality answering "nope, can't do it" when we ask for more Vault space instead of a 30 line poem about decisions and story and attachment and the meaning of life and sorry but not at this moment in Deejspeak. But I'll still be annoyed that I don't like the answer.
The writing style isn't really the reason people have accumulated a certain disdain for Deej, it's the fact that he's the voice for all of Bungie's decisions. If it were Luke or anyone else running the CM job, no matter how cool the tone, people would be tired of getting shut down or ignored by now.
While it seems like the problem is Deej, I don't think personality would change much. It's a job that's gonna get you on the community's nerves eventually just because you're the face associated with requests and delays and disappointments and unfixed glitches etc.
So even if Deej did a 180 and started actually answering shit (including answers like sorry can't say, plain and simple) it wouldn't make people suddenly love the guy.