Hey, I've just completed an analysis of aircraft bin space.
I limited this analysis to two-aisle aircraft (every trans-Atlantic flight I have ever been on was on a two-aisle aircraft). They are either 2-4-2, 2-5-2, 3-3-3, or 3-4-3 configuration. Assuming that these aircraft now have modern bins that are at least 14" high (the regulation width for bags on most (all?) trans-Atlantic airlines, and enough depth that a "regulation" height suitcase can fit in, wheels, or bottom, first, there is more than enough space for every passenger to have at least 9" (usually a lot more) of bin length. That is enough space to fit a regulation size bag. There is plenty of space in the overhead bins for every passenger's luggage.
So, why is there a problem? Considering that over half of passengers check their luggage, there should never be a problem.
But, I've seen some people try to bring onboard a carryon that is too long (more than 22") to fit in the overhead bin across the cabin, i.e., wheels or bottom first. So they have to put in in sideways, where it take the width for 2½ normal bin users.
In my opinion, any bag put in sideways should be taken out and shredded, or at least put on the next flight to the destination. Ok, at least gate checked at a higher fee for the extra service.
Maybe airlines should have kiosks installed in all of the gate areas. Passenger put their "carry-on" in the kiosk, wheels or bottoms in first, wide side (14") down. If they can't close the door of the kiosk, red lights flash, sirens blared, and gendarmes appear to take them to the place of execution. OK, maybe not, but they can't get approved. After they get the door closed, platens come in from the sides to make sure it doesn't exceed the maximum width. Then a platen comes down to assure it does not exceed the allowed cross-section, 14"x9" or 126 sq in.
If your bag passes, it is automatically affixed with a non-removable sticker (color and pattern changes daily, like ski lift tickets) to show that you can carry it on. Otherwise it falls to the floor below to be gate checked with an additional fee, payable at baggage claim.