Reduce hand baggage allowances across the board. As it stands there's no enough space on the aircraft to accommodate everything if all passengers utilise their allowance.
Then enforce it ruthlessly.
Ugh, hell no, baggage issues are bad enough as it is. You realize that people are going to a destination and need clothing for when they arrive, right? I never understood that about those LCC fares that only include under-seat storage. And all it does it increase fees as people now have to pay for hold or overhead bin space.
In my opinion, the answer to easier boarding is to give everyone one roller bag - either in the hold (any allowable size) OR overhead (standard size). Of course the tracking logistics of that are complicated, and the airlines would rather gate-check the bags when the bins run out, than give up those hold fees.