As for payments slowing down boarding: I expect that it does, but the price info I see online suggests that the carryon fees are punitive (more than checked baggage, and with a 100% surcharge for paying at the gate). In other words, the purpose of the fee is more about discouraging people from bringing a carryon in the first place than the revenue it generates.
Frontier doesn't seem to be shy about reminding customers about the gate pay surcharge, either.
> How would they charge for carryons though? Would they charge for say a bag of food you just bought?
Simple. Charge for the right to put a suitcase in the overhead bins. If it can fit under the seat in front of you, in the seat pocket, or if you can wear it, then no problem.
> Also they'd have to put in infrastructure for charging right at the gate
The flight attendants already have the ability to say "sorry, you need to check that" if the bins are full or if an item is too big, and then get the item where it needs to go. They already have the ability to charge your card with a handheld reader if you want to order special food items. I'm failing to see the obstacle here.
getting rid of the carry-on doesn't mean no personal item, it just means you aren't allowed any space in the overhead bin.
If I chose to not bring two items (or three, or four, as many passengers do because there is no enforcement of rules), I should get to place it in the overhead bins and not have to cramp my feet.