Thanks for empahsizing that point, Christopher. I wanted to state something similar, but you stated better than I could have done. We start to see a shift by the conclusion of part 2 of "The Edge of Destruction". At least he acknowledges Barbara and Ian are not "dead weight". I have not examined what survives of "Marco Polo", so I have to ask; does he become more involved in that story, or is it later?
So taking those aspects into account, the Doctor does not leave Gallifrey to "save the universe". That came later. He "fled" (though he claims 'exile' in the earliest serials).