It would be perfectly reasonable to say that a degree of computer control is involved and the delay is purely down to the crew trying to make sense of the sensor data and pick out particular targets. So in other words both PD (and maybe free fire mode) could fire in a very rapid sequence in a coordinated fashion that doesn't involve humans but also doesn't involve human decision making as to target priority.
I don't even thing that an advanced AI would be able to shoot... assess battle damage and then assign an new target all in a five second time frame... that would require some sort of advanced knowledge of the outcome in advance.
It is more realistic that fire are done per five second increment... even being able to asses battle damage in just five seconds to know if something is destroyed/damages and how much is asking allot to be honest.
It is a game and I understand that some measure of abstraction need to be done. I guess this is more to do with wanting efficiency not really being realistic. Personally I like the issues with simulation so I'm in favor of more obstruction to picking targets in general.
I would agree with you if battle damage assessment appeared to have anything to do with crew, but it does not it is instantaneous for all intents and purposes. Also generally if the target separates into multiple pieces you don't need AI to figure out it was destroyed and modern radars are capable of figuring that out without human intervention. What you are suggesting is fairly old fashioned and unlikely to really be a thing in the future, let alone in a fully space faring civilization.
Battle damage assessment in the game is not realistic... it is a convenient abstraction for ease of play. It is physically impossible to get that accurate battle damage assessment within that time frame in reality no matter what technology you would be using.
A ship does not have to actually explode to be a complete loss, so knowing a damaged ship from a lost one could be very difficult to know in real life, especially in space as they don't "sink" anywhere.
The fact that crew can get to the escape pods in a five second increment also is unrealistic and just an abstraction of the combat mechanic.
You could try and play games such as "Command: Modern Operations" which probably are as realistic you can get from that perspective on modern warfare. Battle damage is quite literally part of the game and it can take quite some time to know how much damage any type of attack did in many circumstances.
In real life target acquisition outside imminent threat usually have to go through some sort of command chain... if you need to coordinate ships in a fleet you need to respect the command chain to some degree as well to coordinate fire between ships their squadron or the entire task-force or even worse an entire fleet of dozens or more ships.
The fire at will rule... sort of abstract the chain of command away so each captain or weapons officer in charge of that targeting array make the decision on the fly, this is also an abstraction.