Beethoven used to say : "I wish I could write like Mozart". None of them were obsessed, instead they heard a lot of others' and predecessor's music. Brahms wrote many music based on haydn and beethoven's work. They were good listeners first, and composers later. Zubin Mehta once said "Listening helps to develop the ability for music appreciation, the most important quality of a musician". Schumann, Schubert, Berlioz - none were "OBSESSED" with their own work, they were great lover's of their peers' music.
I repeat that a good listener and appreciator, who is much more mature, has the best chances of writing great music. He is mature because appreciating others' music dispassionately and analysing it requires an open mind, a keen sense of responsibility, suppression of ego and a sense of music (which someone aspiring to be a musician should possess in any case).
There are many instances of such here in YC. Just read Morivou's comments in this page :
http://www.youngcomposers.com/forum/string-quartet-g-minor-5343.html
His analysis may or may not be perfect, but just see his sincerity and honesty, and the use of language to avoid hurting the composer while conveying what Morvou really thought. If this is not Maturity, then what is ?