Of course, all airlines could fix the problem with carry-on luggage very simply by installing overhead bins with separators to create a individual compartments of the exact size of their maximum permissible carry-on bag. Label each compartment with a seat number - and presto.
You're kidding, I hope. I can't think of anything that would make worse use of the space available than a whole bunch of extra, expensive, and unnecessary dividers.
The most flexible arrangement, though clearly not possible for structural reasons, would be to have a single bin the full length of the cabin with no dividers at all. Closing it would be fun as well.
It would at least stop a lot of the cheating that goes on (In the states I noticed a lot of the pax taking on 2 or 3 pieces of handbaggage!).
Far better, simpler, and quicker to stop passengers getting past the gate with more than one piece.