I'm actually a big fan of capture-able eagle eye turrets. It's just another objective to fight over, like repair pads, Ammo APCs, and mech bays.
Captureable eagle-eyes gives the ground-pounders an objective, a reason to capture a particular base, or at least destroy the turret. If you're a pilot and ask your team to destroy the eagle eye giving you problems, someone will usually destroy it.
It is not unreasonable for capture-able Eagle Eyes that limit a ASF pilots operational airspace, especially in a map like flatlands where you can fly low to the ground in tight circles to capture undefended grids.
Should capture-able eagle eyes be positioned in such a way to provide cover for the whole map, or multiple Eagle eyes providing overlapping cones of fire? No.
Death Valley does this well with the north and south bases where it has eagle eyes, but there is a mountain in the way preventing them from creating a complete bubble of protection. The East/West bases are near enough the main bases that it gives your team an incentive for taking them, otherwise there isn't much point to those bases.
I really like the idea of walls covering the the turret's field of fire. Then all turrets have clearly determined blindspots. Ideally Lasers are for ground targets, Eagle eyes are for air, and no base should have both.