Bungie seemed hell bent on making John seem like a faceless nobody that you can inhabit.
But the moment they had cortana say his name at the end of halo 3, they basically admitted that he is his own person, with his own history, his own story, he is not you, you simply play as him.
So hopefully 343 explores John more.
But my opinion on why he fought on after Reach: All of his friends and family just died along with his home; Halsey, and all spartans but him (or so he thinks), Reach itself. In a sense, they, heck all of humanity who had died at the hands of the covenant over the last 27 years, died so that they could discover halo. Humanity could have discovered halo at any point during the past century; its location was sitting right under their noses on reach, but no, it took the sacrifice of billions to reveal Halo. Dr. Halsey herself knew that Halo was the great turning point of the war, she even told noble team that they might all have die just for this. John feels it is his duty to all those who died to discover Halos secrets and use it to save the rest of humanity, avenge his fallen brothers and sisters, and avenge the billions of lives lost.
[Edited on 07.21.2011 6:38 PM PDT]