You can increase the level of your generals through affection points, happy pokkuru (from freed prisoners), or from dungeons. These increase the general's level by either 1 or 2.
Sure, it's to experience the story. I think it's a better experience overall when playing the game normally though. You do forget that it's classified as SRPG. It's supposed to be something like that. Also, the enemy territories scale their troops according to your troops. They're supposed to get troops from the air. That's what balances the game's difficulty. You're supposed to adapt strategy, after all. Though I admit that there's not much strategy. Just plan out what you'll do in a turn.
I guess you'll have a heart attack when you see 5-star difficulty's troop scaling.