Agree it can be case by case.
I wasn't diverted, but flying LAX-ORD-GRR. ORD got hit w/ major winter storm & flights before/after my connecting flight to GRR were canceled. Mine showed still going, but I knew it probably would get canceled, as it was continually pushed back, & I'd end up overnighting at ORD. I talked to gate agent & said tell me the truth, do you think it's going to go? Because if not I can scramble into downtown Chicago & catch Amtrak home, but there's only 1 Amtrak & I'll be cutting it close so I pretty much have to know now. I do have checked luggage, but I'll drive to GRR from home & get it tomorrow when flights resume/realize you don't have to have it delivered to me. Agent, said take Amtrak. I got on the blue line & 10 minutes later got the UA update saying my flight was canceled. Of course if I had been in a diverted situation w/ checked luggage, that wouldn't have worked (unless it was a long diversion & they had time to offload luggage).
I've also been in 2 diversions, where one was ok w/ letting us deplane w/ carry-on & one said no.
Cheers.