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Balanchine was certainly a great choreographer and a charismatic person (by all accounts) and you are right, NYC would not be where it is today without him, but on a global scale there were others who had just as much, if not more, influence on trends in ballet than he. I love his ballets, but I think there is a danger in idolising one person to the exclusion of others. In some ways he was very narrow-minded in his 'vision'. I think Fokine and Ashton had a greater influence overall on 20th century ballet.
As far as I can remember only the Royal Ballet kept as many as three of Fokines ballets alive from the 1950's to date. Since the 1980's a Fokine industry has proliferated with his ballets poorly staged compared to those productions I had seen supervised by Tamara Karsavina, Serge Grigoriev, Lubov Tchernicheva, Lydia Sokolova, Nikolai Beriosoff and Dame Alicia Markova.
Of course Fokine formalised via Diaghilev the triple bill formula which had hardly existed at the Maryinsky Imperial Ballet until the 20th century.
The Royal Danes and the Borovansky Ballet kept at least two ballets alive in the 1950's, Festival Ballet had Les Sylphide and even in Russia it was only this work and the Polovtsian Dances that survived up until recent times.
Ashton's influence across the world is due mainly to productions of "La Fille mal Gardee" ably supervised by Alexander Grant a member of the ballets original cast. Two Pigeons is now performed in the USA and Georgia and Les Patineurs has been seen in the USa for some years now. ABT has staged Sylvia and I am sure other posters will tell me there are other Ashton works being performed there. When Ashton ballets have been strongly admired outside London, it has usually been so, when the Royal Ballet have performed them on tour to the USA and elsewhere retaining the correct Ashton style so difficult to achieve.
When the Kirov ballet tour, they have often taken a Balanchine repertoire with them. The Royal Ballet have just been performing Jewels and they have had in my time at least, something like 14 Balanchine ballets in their repertoire. and his ballets are peformed in Japan, Australiam a number of other European countrie exhibiting Balanchine's international influence which is possibly greater than Fokine's and seccond only to Petipa and sometimes enjoined with Ivanov.
You say, "The ballets he composed for were the results of many artists collaborating under the direction of Diaghilev. Who knows....another composer may have done as well!" Balanchine choreographed nine ballets for Diaghlev and to music by seven different composers. Of those ballets, as far as I know, only Stravinsky's Apollon Musagete and Prokofiev's Le Fils Prodigue have survived. Apollo was recognised as a major diversion away from the past and breaking new ground. Stravinsky's score to this work is widely admired. While for all it distinction and I admire it greatly, Le Fils Prodigue does to me looks a little like a homage to Fokine's methodology.
Of course Diaghilev was there with his advisers to oversee Balanchine's productions and this remains a practice to a lesser or greater degree even today. But, as we know Balanchine was a completely original voice established through his Petrograd experience, his music training, nd his sophisticated educated family background and Diaghilev was no choreographer.