Particularly given that:
Artificial Intelligence is not achieved. They have extremely advanced
computers, but not truly (meaning creative, reasoning, inventive)
So you've got good computers, but no true AI. The implies that if the drone runs into a situation it hasn't been explicitly programmed for, it's going to either 1) make a suboptimal/wrong decision, 2) make no decision, or 3) attempt to communicate with an organic operator so that they can make a decision.
The first two outcomes are bad (with the first being potentially catastrophic if the wrong decision is something like 'start nuking friendly cities from orbit; it's the only way to be sure'), and the third doesn't work well even with instantaneous communication (especially if the instantaneous communication mechanism has a finite maximum throughput), as for an organic operator probably nothing is as effective as actually being there and seeing everything with your own optical receptors. A program that can't solve the situation for itself may also be unable to solve the problem of what information is actually relevant and important to solving the situation.
Resistance to Hijacking
If the drones can respond to instructions from an external operator, which I think is something they essentially must be able to do in the absence of true AI, they're vulnerable to technological hijacking. Your enemy doesn't have to fight your drones, they just have to reverse-engineer your communications mechanism or covertly take over one of your comm stations while your drone army is out looking for the enemy army. Then they turn your drone army against you, and it's game over pretty quick (unless it turns out that organics are actually superior fighters after all...meaning that in either case the drones were a bad idea to begin with).
At least with traditional ships piloted by organic crews, the only way to take one over is to actually face it in combat, overwhelm its defenses, and subjugate or kill its crew members. All while preventing them from doing something inconvenient, like rigging their ship to explode and take your boarding party and half your moon out with them.
Resistance to Damage/Increased Autonomy
Similarly, if the drones are reliant upon external operators, you've now given your entire army a very obvious weak point. All your enemy has to do is come up with a way of disabling (or jamming) the communications subsystem, and the drone is robbed of all external input and left to rely on its advanced but non-sentient computer programming. Making it still potentially dangerous, but also potentially easy to then completely disable by exploiting some flaw in the program (may be hard for your enemy to find, but it only takes one). Then they can gut your drones for material, or perhaps even reprogram them and send them back against you.
With embedded organics each ship is able to operate autonomously, even if communications are disrupted or disabled for extended periods of time. They can be cut off while continuing to pursue their mission independently, which is something that appears to have even actually happened.
You Can Still Have Drones
People are useful for the operational decision-making, and harder to subvert through technological means. But drones are small, numerous, expendable, and not burdened by having to devote significant space, energy, and mass to superfluous luxuries like life-support. Any ship that's capable of supporting a sizeable organic crew can also carry a large complement of drones.
So why not have both? Use the organics for the decision-making and operational concerns, and have them man the big weapons-systems, and have fleets of drones that can be deployed for things like point-defense, skirmishing with enemy warcraft, mining resources, search-and-rescue, and similar tasks. Drones could certainly be effective at all of those things without true AI, and with the organics on the ship only needing to direct them at a high level like "mine that asteroid" or "intercept that fighter group". Then you get a lot of the benefits of a drone army, while mitigating some of the most significant weaknesses of an all-drone approach.