That doesn't answer the question....?
The question is - can you ONLY earn experience by competing objectives?
If so, that means you can only earn XP from the 3 Daily objectives, once you've completed all of the currently released Ultimate Alumni, Conference Stories, Legends, Season 1 & ICYMI objectives.
If that's the case... how are so many people claiming they're max level already? Or seeing streamers that are way ahead of the level you should be right now, assuming you only earn XP via Daily objectives, for the most part.