I witnessed this in LAS last month. Gate agents had made multiple announcements that they needed to gate check 15 bags or boarding would NOT start. They kept making multiple announcements as a count down, I don't remember how many times. When someone asked if his backpack would count, boarding agent said, doesn't matter, any bag will do. These bags were tagged by gate agents and sent down at the gate. If this were a weight thing, why didn't they ask for bigger bags?
Boarding was definitely delayed. Rather than boarding 30 minutes prior, it started like 10 minutes prior. Then they ran out of overhead space and backed everyone coming on board to jetway (at least another 10+ people). They said everyone standing had to gate check their bag. One guy offered a $100 to anyone willing to check their bag and give up their overhead space. FA told passengers to leave their bag and they would find them with "handwritten" bag tag. This delayed plane even further. Seemed kind of hap hazard how they did it, how would you remember which passenger had what color bag? Most didn't have boarding passes in hand.
When we finally taxied away from the gate, we were stuck in a queue of planes waiting to take off. It was the worst run as there seemed to be no urgency to close the doors as we already missed our slot. Landed 32 minutes late. I'm sure some of it was made up in the air.