I think it depends on the GA.
Mrs BHammy and I were headed to SYD through ATL and LAX from CHA...two weeks after I had back surgery.
I had an earlier flight to check gear through customs in ATL (with carnet), wife was coming 3 hours later with a tighter connection (45 mins, I think)
We were both PMs at the time, got seat in the second row of C+ just inside boarding door, and FA closed bins above us knowing she was running late due to weather out of CHA. My wife ran to the gate, with a CabinOK sized bag (smaller than normal carry on) which had ice packs and such as well as feminine products for our 4 hour flight to LAX and then 14 hour flight to SYD.
But within 15 minutes of closing the doors, the GA flipped on her power trip mode: ALL FURTHER BAGS MUST BE CHECKED.
I could hear my wife and several other pax in the jetway pleading with her to carry on small bags. "NO - or you won't be flying" was her only reponse.
She hadn't checked with the FAs what so ever - she only wanted an online gate departure....ended up taking WAY longer arguing with pax, getting bag tags, fragile tags, etc... My wife ends up coming on board in tears having to carry her feminine products onboard by hand, with the FAs shocked at how the GA was treating the last few pax.
During flight, FA ended up apologizing for GA, gave my wife a selection of premium snax and bottle of wine.
Post flight complaint ended with stock response covering for staff.
That's been the worst of our flights - but when showing up 'late' (zone 3+) to the gate, I hear more and more about checking bags. They let us on, both the DM status now, but plenty of others are stuck putting their bags below to destination. YMMV.