I think it is a great idea. I would add that the story should allow the character to earn gear specifically for that character and once they finished the story mode they would have enough to completely level, gear, ability and mod them.
The story mode should also have the same training tutorial techniques like the ones they've done during events that help train players on the most effective way to master them and promote the right squads to use them in.
Included in the rewards could be additional unique currency to purchase more items like gear, shards, etc... or perhaps even things that you can't buy in other shops like crystals, energy, other shop currency in the story mode.
The story modes should be accessible as soon as a player unlocks them.