The decision of revealing secret information is based first upon the classic conundrum of intelligence work. Using secret information always carries the risk of the enemy becoming aware of the infiltration. In this case there is no risk of it being known, we will essentially tell the highest echelons about it. There can only be one result coming from this, and it is a crackdown. This means we could easily lower our current T-4 spy network, through this reveal, into a T-3 or just T-2. The Empire had a ruthless, backstabbing, intrigue plagued corporate culture. No one that gained a high rank in this climate would not act upon learning his own state has been infiltrated in such a way. He will overhaul his counterintelligence measures, and this will hurt our spy-network and future prospects there. Ignoring how this could lead to others doing the same in the worst case scenario.
Therefore, the simple question that follows is, is it worth it?
The only purpose of such a revelation would be to change our threat potential. There is no difference to our economic weight or other arguments regarding trade, but the threat potential of the Empire of the Hand would be changed. Before, Kaine was quite sure of himself being in the stronger position, but with such a revelation, doubt starts to set in. What other aces does Thrawn have up his sleeve? This question will trouble him and the threat potential goes up. Contrary to our diplomatic measures, we now appear threatening. Because what else do we know? His secret projects, potential scandals, plans or do we even have allies in his ranks...and the paranoia will run away with it.
And what would we gain from that? Would he invest more into someone that now appears threatening? Hell, no. Would he hold himself back and offer a better deal? Maybe, it is possible.
So, is it worth it? Hell, the fuck no! For a slightly or even just better deal we would be on his radar as a potential threat, we have revealed our intelligence arm and infiltration of his state leading to a crackdown and more problems gathering intelligence from his realm in the future, revealed our diplomatic moves to be mere smoke and mirrors and lastly made him feel like a fool.
Threats, and nothing else is revealing the infiltration of another state, never lead to improved relations between states, but the opposite. Kaine wants to have fewer enemies and achieve that through trade. This is wholesale advantageous to us, we play the long-game and not the short one. His current intentions towards us are peaceful, there is no need to roll the dice upon this sentiment.