I am not sure what the point is in perpetuating this falsehood. The dimensions of the standard Brompton are
23"x22.2"x10.6" yielding the linear dimension of 23+22.2+10.6=55.8" well under the standard airline limit of 62", leaving room for walls of a container, rack and any accessories. Yes the Radical Design Chubby blows the airline limit pointlessly. The airline agents may let it through, but I returned mine, not wanting to take the risk. As to Birdy, most people that comment online appear to take it apart for flights. I did it for Bike Friday and Dahon and pretty much had enough - with this much work I could well take a regular bike along.
Te folded size of the Brompton and Birdy and several other folding bikes depend of the mounting of the saddle.
The size given by Brompton is very optimistic, its with the saddle mounted on a position that minimize the folded size, i.e. pentaclip in front of the seat-pillar, saddle advanced to the front as much as possible and mounted on the lowest position on the pentaclip, a configuration that only fits for short people. Then, the folded bike fits into the airline size without any case around it, in a soft bag snug around the folded bike.
Of course, its with the standard seat-pillar that fits only for people up to about 1m75 and less when the saddle is mounted on the lower position of the pentaclip. People above about 1m75, need a longer seat-pillar that increase the height of the folded Brompton.
With an average cyclist, the folded Brompton is bigger and its the reason why all cases made to carry the folded Brompton are too big to fit in the airline limit. The folded Brompton without any dismounting doesn't fit in any airline compliant case. Its also the reason why the Chubby is bigger.
And its the same for the Birdy, the size given by Pacific Cycles is for short people, the bigger one given by Riese & Müller for taller people.
My comparison picture show clearly that for both bikes the saddle position has a major impact on the overall folded size. Removing the saddle+seat-pillar greatly reduces the folded size.
Last point, how often do most people fly with their folding bike?
In the daily life (putting the folded bike in a caddy during shopping, carrying the folded bike in public transportation, taking the folded bike inside shop, cinema, hospitals, elevators, storing the folded bike under a desk...), the little difference in folded size between the Brompton and Birdy doesn't really matter.
About the Sunrace hub and cassette mounted on the Birdy Touring: I never experienced problem with it, it shifts very well with a Shimano derailleur and it has been realiable for me.
But, its a proprietary solution, the hub accepts only the Sunrace special cassette and this cassette can only be mounted on a Sunrace hub (and maybe the now discontinued Shimano Capreo that R&M was using before the Sunrace solution). These Sunrace components are pretty difficult to buy if not from a R&M dealer (that must most of the time order it).
On my Ti Birdy, Pacific Cycles mounted a standard Shimano rear hub with a 11s 11-28t cassette (both Shimano 105), the range is quite short and the longest ratio too short (front chainring is a FSA SLK-light compact 52-36).
I therefore looked for another solution and moved to a new rear wheel with an XDR body rear hub and Ethirteen made 11s 9-32t cassette (the previous generation Shimano Ultegra RD-R6800 derailleur I have is limited to 32t max).
When the cassette of my Birdy Touring had to be replaced, I did the same on my Birdy Touring that has now an 11s 9-34t Ethirteen cassette and Shimano Ultegra RD-R8000 derailleur. I hesitated between this solution and a SRAM Force Etap AXS 12s and 10-36 cassette but since it is a daily used utility bike, I preferred a mechanical rear derailleur.