IMO it's chaos either way:

If they don't charge for gate checking, people will try (even more) to take additional carry-ons. Regardless of if the pax gets caught and has the bag checked for free or if the bag ends up as carry on, the pax comes out ahead compared to waiting in a check-in line and paying. Result: longer lines at security and chaos at the gate.

If they do charge for gate checking, there are going to be some seriously irate pax when they are forced to gate check their bag due to late boarding, particularly if it is due to a late-arriving connection. The pax will have a point: they brought a legal amount of carry-on, which possibly has already made it through one flight, why should they have to pay because the airline either didn't have enough space or didn't get them to their connection on time? In addition, gate-check charges will mean extra work for gate agents at the busiest moments just before they close out a flight. Result: chaos at the gate.

IMO these bag check charges (for the 1st bag) are disasters waiting to happen which will hopefully flop miserably. In addition to other problems, I find it unconscionable that airlines are allowed to charge for checked bags when TSA bans harmless items needed for everyday life from carryon, such as cosmetics, toiletries, etc. At a minimum, the airlines should be required to allow every pax to check for free a single bag up to 10 lb or so to deal with the (idiotic) liquid ban.