It's "sadly" intended which forces you to pick which battle you want to use your dragon in to be at an advantage.
Personally I think there should've been a way to increase the number of battles you could do yourself per turn to 3, but to each his own I guess.
You have to keep the fact that you can only control 1 battle in mind as you progress. Basically meaning, try to minimize how many battle are fought each turn as much as possible and always take control of either the most crucial battle or the battle that's most likely to lose.
It's funny that you didn't notice this till Chapter 3 lol.
A funny strat you could do that would circumvent this restriction is build as big of an army as you can and have it bumrush it's way to the enemy capital without care of defending lands you take over en route. Cause afterall you only need to capture the capital and hold it for a turn to defeat an enemy.
That's kind of lame really. I could understand not wanting to let us rts it out for every battle, given that its hard to lose with the dragon. But 1 per turn? That's a little weak...
And honestly, it never came up before ch3. Didnt need the dragon at all in ch1. In ch2 I insta-rushed the guy who spawned behind me and took him out on the first turn. The rest was all landing parties and slow-pushes through the mainland. Ch3 is the first time ive actually had more than ~3 battles happen in 1 turn, and its also the only time ive had an actual troop disadvantage 0.0