Refitting a station is kind of a lot of work, and you'd probably feel obligated to do it before every fight in which you had one on your side, either to counter the specific enemies it's facing, or to update its weapons to match whatever latest blueprints you've got. If you couldn't refit instantly (i.e. it took some time for a new fit to take effect), then you'd have to proactively update the loadouts any time you got a better blueprint; that seems possibly even worse.
All this for a fairly limited number of fights where the station is on your side, and its loadout doesn't really affect that much, beyond making it weaker/stronger. I don't think the amount of player-hassle is justified by what you'd get out of it. Heck, I don't think it'd be justified even if you got a lot more than this out if it.
Kind of the same argument applies to colony-spawned fleets, really. They're ... not free, exactly, but they're a lot cheaper than the ships in your personal fleet, both in terms of credits and time invested. So they kind of get what they get; for auto-resolve it doesn't matter, and when you're helping them out in a battle, you don't really care if they sustain some losses, and the core of your fleet is customized and will do most of the work, so... there's just not much point to having detailed fleet customization for faction-fleets, imo - what's there is mostly for feel reasons.
Also, as far as stations go, Morrokain brings up a really good point - balancing modules for actual refit would be... a problem. Right now, they're not set up for this at all; e.g. under the hood ordnance points are virtually unlimited, flux values are more or less fixed, etc. So even if it were desirable, it's far from a question of "just" making station loadouts customizable. They're not built with this in mind.