I've created my own (probably crazy) excuse for the AI's apparent stupidity.
You probably noticed the "sensors" icon is a camera, right? And that your ship is the only one which targets single locations on enemy ships with multi-shot weapons? How about the fact that, while your ship has a full crew, there is no apparent Captain on board, and no matter which crew members die, you can continue the mission - even if every one of your starting crew is wiped out.
My theory is that your ship IS the message. You don't play as a crew member or a living Captain - you play as the ship's AI. This explains the importance of getting the ship itself to the Federation fleet, rather than just scattering the crew across every jump-capable ship you can find to make sure the "message" is delivered in time. It also explains how you're able to target precise locations on the enemy ships - your AI has a database of known ships, a limited ability to hack into enemy ship's systems to confirm the locations of key systems. This can be upgraded to initially allow a view into the enemy ship by hacking their internal camera systems, and later to also access the more secure systems monitoring the ship's power management.
This way, it makes sense that while you precisely target the enemy ship's critical locations, they seem - with their living, error-prone gunners (or simplistic AI in the case of auto-ships) - incapable of doing the same.
It also explains why - after traveling such a distance through all those hazards, they still expect YOUR ship to fight the Rebel Flagship. Nothing else can find the weakpoints needed to disable it efficiently.