Tell that to the Romans. Or Attila. Or Genghis Khan. Or the Vikings. Or the Normans.
History is filled with cultures that imposed their values on others very successfully. However, that first requires that you believe in your own culture.
Unfortunately, cultures whose values are being visibly undermined daily will have trouble imposing them on those who are willing to destroy other cultures to impose theirs.
There was a time when America had the will to wipe the other slate clean(er), too.