This is more of a war thought for dragons, and I admit it would need some trial and error math on cost and health to be done.
You have just released a giant fire breathing viscous man eating snarling beast onto the battle field, that could and probably would bite both sides.
So I was thinking making them more like a ritual, where you only have so long to launch it and it eventually gets bored and wanders off.
Instead of the dragon just having a flat effect like -10% BE, it could have an on tick effect, like attacking a random army which is currently not home either from or against the affected kingdom. Like a ritual the amount of resources put into the dragon could make the effect better for the person funding the dragon. Not funding it at all would have the kingdom you sent it against with a small, like 25% chance to have one of their armies attacked and a 75% chance to attack the army of the sending kingdom but with a fully funded dragon having the reverse of a 75% chance of attacking a target kingdom army and a 25% chance of "accidentally" attacking an army of the sending kingdom. It would kill a % of the army and the dragon would then lose health based on the army it attacked.
I also had the thought of diversifying the cost to include food or soldiers to launch it but that is another thought entirely.