This issue is a big problem for me because I prefer to organize my fleet into discrete combat elements, generally a cruiser or capital escorted by some fast destroyers. I do this so my fleet remains both mobile enough to avoid engagements it can't win, but also dense enough that the large ships can't get flanked by frigates without a fast destroyer nearby to fend off the flankers. If one of those cruisers, escorted by a pair of destroyers, runs off after a lone frigate it can't quite kill, then that's about a quarter or a third of my combat strength running off to do nothing; much like what happened in the video in the original post. Being a human, I can tell the AI to stop doing that and get back to their job, but unless I catch it immediately then they've still wasted a bunch of time and have to travel half the combat space to get back into the fight. Doing so also wastes a Command Point, and those things don't regenerate.
On the short-term, individual ship level, the AI may think it's doing something good; it's in very little danger and it's going to be able to destroy part of the enemy fleet. Low risk, moderate gain. From a long-term, fleet-wide perspective, it's risking the rest of the fleet being overwhelmed while it's not there in order to kill a single frigate that may not even have strike weaponry. High risk, low gain.
Other people have mentioned this, but I wish to reiterate that the individual ship AI is quite good in a 1v1 context between equal-ish ships. It's somewhat unable to tell when it should be cautious and when it should engage hard, but that is a difficult problem to solve. Though you have solved it for when to use missiles, as the tournament demonstrates nicely. However, it doesn't stick together enough in fleet actions, and the escort order seems to be more of a "protect this ship with your life" order rather than a "stay close when possible and support each other" order.