I think when people say SAA, they are thinking hollywood more than history. When you watch an old western, every cowboy has a SAA, and this is fictitious but when you see a WWII film where nearly every US soldier that has a pistol, has a 1911, this is real. The SAA was issued WITH the schofield, showing it could not dominate its contemporaries the way the 1911 did. Also, it was surpassed quickly compared to the 1911, and in a meaningful way - SA vs DA, swing out cylinder vs loading gate.
The 1911 also arguably did much more for the country, and is more popular today, than the SAA was for its centennial. Even with the SAA copies, the 1911 still has more, and is a good enough design to be ordered by the USMC.
When I say America's sidearm, I mean in all respects: origin in this country, caliber origin in this country, how original the design, how long it was relevant, how many were made, how long it has been popular, how it was judged against its contemporaries, domestic usage, military service life, functionality, reliability, etc.
Winchester 73, the TFL user that won the west