We will be flying to Houston soon w/my new Martin in one of their older blue "airline-proof" stoutly built molded cases, which they apparently don't make any more; Used to fly w/the old Ovation, whose case is thicker but a little shorter & narrower across the bout; it always - for years - fit in the overhead laying flat -easily. The Martin is slightly longer & wider & needs to be tilted up slightly to fit, but it DOES FIT in the overhead.. We are going for a gig so I don't want to take the Baby Taylor or borrow a guitar.. & I've seen luggage handlers do bad stuff...
Some years ago flew to Heathrow w/a small OO sized guitar & they also let me take it on board. The only crap I've had in recent years (so far!) was w/the Baby Taylor last year (go figure!)... We'll see what happens this year... But, my experience for some years is: go w/the guitar but take it on board; it WILL fit in the overhead of any modern passenger jet; Their shtick is usually that it should "fit under the seat or in the overhead." Well it DOES. At least up through a typical dreadnaught if the case is trim; haven't tried a Jumbo.
One caveat, though: the new regular "hard shell" case that came w/the guitar is definitely notably bulkier than my Martin AP case, as are other kinds of newer dreadnaught cases - and, I suspect, not as strong as mine. I think to get a stronger case, you'll have to get a custom made very bulky thing.. & IT won't fit in the overhead, for sure.. a sort of catch-22.
Cases, like motorcycle helmets, can approach protection through strength & resistance to deformation of the shell, w/moderate padding or a hi-volme padding approach, w/a somewhat less rigid shell, which seems to describe all of the newer factory cases I've seen. (Or both, which describes the after-market supercases; they're HEAVY!) In either case you want to distribute any forces which impact the shell over a wide area & possibly prevent penetration & minimize injury. Both in helmets & cases I like the first, trimmer approach.
I think there's a role for a well made, not too bulky injection-molded case w/a very tough & more ridid (but not brittle) shell, that could be stronger than any of the newer typical factory cases I see nowadays & less bulky than the after-market monster supercases. That would describe my old Martin AP case, (& some of my favorite MC helmets), but not the newer ones I've seen.