Oh, all those solo missions are also force level synced, by the way.
So you're solo, and you can't be past level 12 for the level 10 mission, past level 17 for the 15 mission, etc. If you are above that level, you're level capped during the instance in question. AND solo.
This means you cannot leech your way through the story, period. You can lazy leech to level 50 but if you want to actually play the game and get goodies, you have to do the work yourself, at least during those early levels.
As for why they haven't added the story past the level 20 stuff, it's because of spoilers.
During alpha and beta, they had a lot of the cutscenes completely blacked out too, either because they weren't finished with the actual movie, or because they didn't want you to get spoiled watching it.