Brees is 5’10 at best. But yes, he’s listed as 6’0.
Frankly, teams fabricate their height so I’d say all “6’1 or 6’2 qb’s” are somewhere between 5’10 and 6’1. Anyone who’s played football knows how grossly overstated height and weight are.
Brees is officially 6' tall. NFL teams are unable to lie about height and weight for players that went to the NFL combine because combine officials take official measurements that are available for anyone to view. Brees actually measured slightly taller than 6'.
Theismann also insists he was 6' tall when he played. He says he has lost 3/4" over the years and is currently 5'11.
I point this out because you seem to be sticking to a point when you don't have to and the evidence doesn't support it. You picked "under 6' tall" as the benchmark for being a short QB when the real benchmark has been more like under 6'1". For example, Brees definitely is 6' tall but he has always been considered a short QB.
And, unfortunately, there haven't been countless all-pro QBs under 6'. It doesn't look like Russel Wilson has ever been an all-pro but he has made several Pro Bowls (they aren't the same thing). He does, however, have a very good chance of being named all-pro this year and he will likely be a HoF'er if he continues on his current path.
Flutie was never an all-pro but he did make the Pro Bowl in 1998.
Sonny Jergenson is really the one guy who definitely fits the bill. He was 5'11" and is an NFL HoF.
Having said all that, I mostly agree with your overriding point - shorter QBs are becoming more and more accepted because of the success of Wilson and Brees and college superstars like Kyler Murray which means height is likely going to be less of a factor when evaluating QB talent moving forward, but the incorrect info that was being thrown around in this thread to prove a point was a bit much.