Iconic is actually a difficult term...As noted by others, patterns such as Sodbuster, Barlow and Stockman all have their ancestry in Europe due to the influence of Sheffield and Solingen and cutlers emigrating to the US. Add this to the huge and expanding market in America at the end of the c19th early c20th and you set the stage for the popularization of patterns and 'iconic' emerges.
For me as a European, the 'iconic' American Traditional is the Trapper and I suspect it was and is hugely popular in N.America as part of the outdoor ethos and Frontiersmanship etc. It is much less appreciated by users in Europe Ironically, it is perhaps my least favourite Traditional pattern but Congress eclipses it! So it gets my vote for 'iconic' or quintessential American pattern.
Nothing wrong with trying out patterns with RR. and using them. I do find their smaller knives better than the large ones personally but to the OP if you want an 'iconic' American Traditional (rather than folders which can encompass all sorts of knives) Du måste köper en CASE kniv och snart!
Thanks, Will