John Stamos is a talented man. Anything is possible in terms of what he will be known for in his career. Before he was known as Uncle Jesse he was known as Blackie from General Hospital. While I do think people will always associate him with that role, there is every possibility in the world that he can become well known for an even larger role.
In spite of our culture of celebrity, most actors and actresses are known for one signature role. Most musicians only have one hit song instead of an ongoing career. It is very likely than John Stamos' most famous role will be on Full House, but it had a long run and it is likely paying him good royalties.
I think the love for Uncle Jesse depends on your particular age. If you were a teen or young adult when Full House ran, then John Stamos will always be Jesse in your heart. John was Blackie before that, and several characters after that, but Jesse was the man. He was a little 'bad boy', but always did the right thing in the end. Jesse was all sorts of handsome, but was also just as sweet and protective. As we grew with Jesse, he became a great father and husband. Uncle Jesse was the full package in a young girls heart. No matter what John Stamos does, that feeling in your heart will always go back to the perfect Uncle Jesse.
The Full House character of Uncle Jesse will live on forever. Everyone will remember his dark long hair and his tight outfits and his band, Jesse and the Rippers. He was attractive back then and has only got more attractive as he has aged. Uncle Jesse made him very famous!