I don't think that Russians see any less value in skating skills and performance qualities than anyone else. Trusova, for instance, never got PCSs like Shcherbakova despite being the original quadling. plus she skated with Russia fire in her belly.
About cultural influences, my opinion is that this is subtle and, point-wise, not a very important consideration when it comes to who wins a skating contest. Hanyu's Seimei program obviously will have greater meaning to Japanese audiences than elsewhere, but still, everyone connected to skating acknowledges this program as among the very finest ever skated.
Patrick Chan's Take Five, to the definitive "cool jazz" tune of the 1950s, wonderfully captures the spirit of the "cool dude" that is so popular in North American folk culture. People who are not into coolness, well, they probably don't think the program has a theme at all.
Michelle Kwan's choreographers tried to have it both ways. She never skated to music with an east Asian theme, but she did play up the "exotic beauty" that Americans and Europeans associate with the Middle East -- Salome, Scheherazade, The Felling Begins. It worked for her (although she was far more popular in the U.S. than internationally).