There are several reasons you might want to
1) If you ever want to decrease your influence in a system - to avoid an unwanted expansion, for example - having an opposed station you can trade/cartographics into can be much more convenient than running missions for the other factions.
2) In the event of a Lockdown, all your controlled stations will stop offering missions. Stations you are present at but don't control will still offer missions, including anti-Lockdown missions.
3) Non-dockable surface bases are mostly a liability - they attract skimmer kill and other missions which give you negative BGS states, but don't really give you any advantages.
It depends what your plans for the system are, what its assets are, where it is, what its population is, and so on.
To 1:
While this is correct in general I personally think that if you are
Allied with all MF in a System (minus except Anarchy unless you can boost your Rep with them via a War / Civil War) it leads to overall better payouts. Which in turn gives your Wingmates a bigger incentive to work the BGS.
Also to leave one asset in the hands of another MF is (like many other things) a double-edged sword. If that Station is supplied heavily with Exploration data then it'll be easy for to bring your MF into unwanted conflicts. There also can be a case that the MF controlling said Station is in armed combat elsewhere, making Trade/Cartographics unusable.
To 2:
To avoid a complete standstill it helps to have at least one System where your MF isn't in full control. So there you can use the open assets to increase / decrease your or another MF to equalise and thus make a conflict pending. The
Lockdown will be gone in 3 days after.
To 3:
Nothing to add.
Thanks Ian.
The latter situation probably fits better and makes a tonne of sense.
It's a system out on the border with 3 assets, one orbital outpost, one dockable planetside and one non-dockable planetside.
At best I should take the orbital and the dockable planetside one as I can then dock large ships at it?
You probably will end up taking the orbital one first and then the ground Port, provided both belong to the same MF. If they have different owners and you only want to have the ability to land big ships it'll be good to get into a conflict with the one holding that one and leave the other be. Assuming you don't want System control but only somewhere to land at that is.
Also it's noteworthy that all Low-tier states (Famine, Outbreak, Bust, Boom, Civil Unrest, Lockdown) can be worked against in their pending phase. If your side can do more then the opposition it results in them not going live or even get completely nullified.