Gonna side with "no" here. Not stations, not planetary cities, not even orbital outposts.
Think about this - we've had community goals to construct these - how many tons of how many materials had to be delivered?
What is the total credit cost for those materials?
Because these would cost at least that much, likely much more.
And that's just the beginning of the expenses involved. There's a reason these belong to factions and powers.
BUT...
A player-owned Hanger/Omni-sized landing pad where you never have to ask permission to land - sure, I'm down with that. Stick it on a planet, or inside a hollowed-out rock somewhere, absolutely.
A couple add-on structures to go with it - a place to sleep, spray the funk out of your RemLock suit? Change your socks? For sure. Another small structure to store materials, maybe a few tons of personal cargo so you can change ships, or keep a souvenir Ancient Relic, you bet.
A trophy wall to display your trophy achievements (that Hutton Mug you picked up, or whatever), yep, definitely - especially with a PS4 release lurking.
Perhaps your own repair and refueling bays (higher costs than at a station, but you pay for convenience).
But really, that's it, that's all they should do, all they'd really need to do.