I agree, but the airlines can also be more proactive: if a flight is 90% full and most pax have not booked baggage, it is obvious that the overhead bins will be overstuffed.
So instead of the gate-check system, which always feels messy, why not proactively send an email or SMS to selected pax; e.g. families, who would actually like to check in if they could do it for free, letting them know that the flight is busy and if they would like to drop their bags at the checkin counter they can do so for operational reasons.