If you ordered the destroyer to capture the point, the game did not register it as Capture, but as Rally. Except if you mean it otherwise? Because if you check the videos I uploaded, even trying to assign a Destroyed to capture a point, by right clicking on the capture spot, the game considers it rally of your forces and not capture. That makes your ships go towards there, but not care enough to capture the point. I have looked up close using the capture command now and indeed the fighter/frigate goes to the point and parks there, trying to not move for the spot.
I have not really use the assault command to capture a point, but first marking a spot as capture and then rallying a couple of ship there works quite well. As soon as the enemy is overpowered the ship seem to try to stay on the spot there, while other ships attack the remaining. So indeed I was just doing it wrong. In the video the destroyer I send to the point just goes there and then fights whatever is close. It takes a while for the enemy to be pushed back and for the Sunder ti go back to his rallied point. If you first assign this as a capture point, it is very obvious that the ships try to fight around the point, rather than drift away from it fighting. As soon as not many forces are left really close, the sunder backed up and captured the point. I tested this on the same enemy fleet as the videos.
As you can see in the video, from the beginning the fighters that were assigned to capture the point, try their best even after they get overwhelmed to stay close to the capture point. Later when the Sunder stays there he tries his best to remain around the point. At a moment that he stars capturing obviously if he remained a bit more there he would manage to capture it, but the AI definitely is trying to put priority in being at the best spot probably, so when he gets flanked. But even if he did not capture it all fast, it is obvious toward the end of the video where he finally parks there, that even if close-by a battle is going on, he decides to first capture the spot and then after do anything else.
Finally! I can imagine my Officer before being like ; But Cap'n, you never asked me to capture the point. You just kept telling me to go there. Be more specific next time, like you were now! >.<!