The same can be said for Toyota but who would ever think of calling a Camry an iconic American car?
The Colt SAA (and its predecessors) were used by thousands of American soldiers on both sides of the Civil War, carried for protection by an unending stream of citizens moving westward to settle a continent as well as the soldiers sent to protect them. Consider also the Western, no matter who the good guys and villains were you can be sure they'd blast away (without reloading) at each other with the good old SAA. As a final note it continues to be found in plastic form with an orange tip in the aisle of any store where toys may be found.
I don't think Glock's resume even comes close.
I am speaking of Modern firearms only as I pointed out.
If you want to look at historical guns I would agree the Colt SAA is probably "The" American sidearm. The same way that the Winchester 1894 or the M1 Garand very well may be "The" American rifle.
Looking just at firearms in common use today, I stand by my comments on the Glock. It is almost as recognizable as a 1911 and it is in far higher rates of circulation amongst LEO's and the public. Think about it, the Glock is a hard working immigrant. It is cheap, reliable, proven, accurate enough and easy to get ahold of. There are not too many thrills about it or tricks to using it.