Oxford was the second-ranking Earl at court. His Earldom was the second oldest still extant.
He was therefore due a mighty amount of deference from those on the lower rungs of society. However, there is no evidence that anyone genuinely regarded Oxford as a poet or a playwright of any standing. If you were not one of the very few people higher up society's ladder, criticising the Earl's poetry or any of his actions was likely to end in tears. And Oxford was quick to take offence. So all mentions of his work as a writer, and they are very, very few in number, are bound to be favourable. His title would always demands his name appear first on any list, as it does on that of Francis Meres. His prose is laboured, dull and verbose and his poetic sentiments tend to to be mundane and selfish.
He really isn't a good choice of candidate for the author of Will's work.