Mine looked exactly the same and TSA was zero problems. They spent far more time on the contents of my pockets than on the bike. No seat removal.
From those airlines, I think Southwest explicitly allows for folders. I flew Delta and it was tense and tricky. On many occasions air personnel whether from SkyTeam or other airlines was nasty for one reason or another and if I had a folder in the they would zero in on it in no time. In travel I have to juggle multiple problems and I do not want to add one more if I do not have to.
Besides haggling there is an issue of the bike in the air being put into the overhead while in a thin bag. I just hate thinking what would happen if it were to slip out of the hands or bin. On occasions I was forced to place a folder into overhead compartment storage on trains in Europe, by rail personnel. I hated it and felt it was irresponsible.
I'll have to agree that putting the bike into the overheads requires a good amount of upper body strength and it pays to be tall. It's not an issue for me, I routinely help people get their luggage up there.
As to weight, the Brompton doesn't come close to what I see others packing.