The war AI IS awful. Especially on larger maps. The problem mostly stems from the fact that the AI is very dumb with transports. Like, if it has a transport too far from the war, it will never get used. Rather than looking near its borders for enemies, it checks to see if there is an enemy planet within a certain distance of its resting point, usually a rally point next to the shipyard it was just built at. By default, this distance is only 8 parsecs, or "still inside their borders."
I've made a war AI that tries to tackle this problem, but the larger the map, the less it will help, because they get exponentially bigger, and the AI's transports could be anywhere. Currently, it only works on Huge and below. It gets weak on Gigantic, and forget Excessive/Insane. It's a band aid until the devs fix how the AI finds it's own transports. It needs to go "here planet, send transport."
Of course, a bigger problem is that the AI loves Tiny ships too much, and it won't send transports without an escort. Its love affair with Tiny ships means it often sticks those ships in Transport fleets, reducing its range and speed so drastically that it can't reach valid targets. My war AI fixes this too, though it has a side effect that the AI often had undefended planets, because the only ships it will station as defenders are defenseless Tiny ships. I want to think its faster Capitals make up for it, but this remains to be seen.