Initial thoughts: Could have merit, but I'd have to redesign my strategy. That's not a bad thing though. In general it sounds more fun, so +1 for that. +2 for being able to deploy stronger and usable defenses on outliers in regards to satellite systems with Fact IVs, heavy Fabs, etc. -1 for breaking my shieldwall.
So, to more details.
Instead of adjusting the existing command station, it might be more viable to create a reactor type unit that will allow supply. Using the existing mechanics from the reactors, additional 'defensive control units' would be less efficient, perhaps at a debilitating rate of 50%. You could even have two versions of this control tower, one for 'in supply', one for 'anywhere'.
This allows a few things:
1) Mobile Builders can construct the defensive control unit anywhere, allowing for beachheading and other off-world tactics.
2) If you REALLY want that 'extra edge' in a system, you can get it, but it can be prohibitive in cost and usage.
3) Cures the multiplayer problem by simply having both players build control towers.
Turret balance will include the new factor of control values. Starting with a cost of 1 for all turrets, 2 for snipers, is probably a good start until more effective balance discussions occur. It's not the implementation cost, just the discussion starter.
The Human Home command station providing infinite control could be avoided/dealt with by having it spawn with a non player buildable control tower, similar to Human Home Settlements.
Logistics/Military stations could simply add to the Control Tower values for the owning player for the system.
But, I LIKE the land of lightning!!!! Oh, alright. You're right though, the shield wall is not as 'fun', and soaks up almost all of my defenses so I rarely have much left to defend satellites. Turrets in general will need some buffing, though, I agree.
As to rebuilds, yes, that would be much handier than me having to make sure any of my edge worlds that get constant wave bombardments always have a cloaked transport one system over waiting to rebuild.