The AI will only build one of those, so every planet you have, will advance your targeting and countermeasures by 10% beyond the enemy. Each.
With 20 planets you dominate the AI by 200% targeting and countermeasures.
That seems wrong.
But at the same time, having a bonus building that makes a big empire superior seems a nice touch to me - just not in targeting and countermeasures.
So how about you make military academies one per empire (probably intended, but overlooked) and instead introduce the Union hall?
The Union hall will increase your bargaining power and thus reduce empire build cost and maintenance cost by 1% each.
It will also increase planetary corruption by 1 or 2 % on the planet it is built (of course this is just randomly dropped off my cuff and balanced numbers could well be totally different) and maybe increase your war weariness a little - union officials always being open to kickbacks and seeing your wars as bad for business
.Of course you might argue, that a bigger empire is better anyway, so why bother.
But I have come to like my idea, so I wanted to float it to you.
What other areas would make sense?