I think American gun manufactures have been pretty dominate in lever actions and revolvers. And true the double rifles never really caught on here, but many American gun manufactures produced some fine single shots. Garand also did pretty well with his action.
America and Europe had very different cultures and needs, and that resulted in different ideas regarding what a gun should be. The double rifle's were made for royalty to take on safari in thick brush in Africa and for Tigers in India. The big American single shots like the Sharpe's were for buffalo on the plains. The Swiss culturally are just fanatics about precision. Those differences resulted in different directions in gun design.
One of histories little ironies is John Browning strengthening the action of the Winchester in the model 94 so that it could shoot the .30 WCF (30-30). That gun and that caliber went on to become American icons. What's ironic is the 30-30 and 7.62x39 are almost identical in performance. Basically the iconic Russian 7.62x39 is a modernized 30-30. How's that for irony?
I can't help but to wonder how much influence the 30-30 had on the development of the 7.62x39 (if any)?