Well, they say be careful what you wish for, but here goes.
I wish that airlines would strictly enforce their baggage policies. On every domestic flight, I see people boarding with luggage that does not comply with the carry on restriction. Often it is a piece of luggage that would not fit in the "screening" crate that Thor described above. Other times a traveller has two large carry-ons instead of one and a "personal" item. On this morning's flight, a large portion of the bin above my seat was occupied by a standard sized guitar in its case. It had to be placed lengthwise in the bin as it otherwise would have stuck out. It prevented three large legal carry-ons from being placed in the bin, although there was room for small items, like a jacket or small parcel.
The current policy rewards the more aggressive or selfish traveller who hovers near the boarding area to win the competition with other travelers so he can find a place in the bins, for example, for his two large bags and "personal" item.
It is my understanding that the European airlines are much more strict in enforcing their baggage policy and if a traveller attempts to board with luggage that should have been checked they will take it , check it, and charge a premium for the trouble.
I have a Brompton, and I have seen the pictures of Bromptons in overhead bins and I have roughly measured bins and determined a Brompton would fit some bins but I will never attempt to carry mine on and place it in the overhead. Boarding takes too long as it is - it would go faster and smoother if we all complied with the requirements.