To me, anything that encourages the player to check the map more often doesn't align with the other stuff in combat.
Eh, i'd say that it depends on the player's play style. It's not ideal for a flagship centric build, a leadership build on the other hand...
As for the goal of splitting fleets on the battlefield. Currently, the player (usually) wants two things for his fleet. First : to keep his ships alive. Second : to at least keep the enemy busy. Hence the battle line formation, or deathball when outnumbered. That way, the flagship can flank the enemy and take down one by one the opponent's ships.
The current objectives points doesn't change the thematic a lot. Do i want to send some of my ships to capture and
hold that objective? The bonus is going to be pretty small, and that squad, as well as the smaller bulk of the fleet, will be more vulnerable to an attack. Is it really worth the risk? Not really. With bigger bonus however? Mmmmaybe? A sudden buff could offset splitting the fleet in two, weaker groups. Hence Gothars's suggestion, mine about global abilities, or even Xeno's capturable defence platforms.
It's a risk vs reward situation. Do i want to split the fleet to get +5% mobility? Not really. Change that bonus to a 20 seconds +30% damage, a Pilum swarm spawned from the edge of the map, or capturing a long range space turret? That might be an interesting choice.
Also, to answer Axle's valid concern about capturing activated defence platforms, perhaps something like this?
Maybe one or two points to capture a defence system depending on its size, and obviously the points won't be near the actual station, hence the need to spread the fleet. The defence platforms don't have to be stationary either, could be a bunch of inactive derelicts that will roam the battlefield once activated. Also, probably best to keep the platforms relatively small for balance purpose.
The biggest issue with all of those : it's a non negligible amount of work for something that works well enough already. Tweaking a few numbers is one thing, adding some new mechanics and thoroughly testing them is another.