I think their impact on the galaxy and game needs to be pretty passive.
They should probably be unarmed and invulnerable, to stop people from trying to use them as weapons platforms, but equally stop people trolling for offline players and blowing up their ships.
I like the ideas stated here previously of being a focused craft/mini game for a squadron. You need to start off with a small one which can be purchased outright (as money if the only thing players can horde in any quantity). But after that you can donate resources, credits, bounties, warrants to the carrier which can then be exchanged for an upgraded ship. It would be good if they could figure out the multiple ships per landing pad thing, and make it more like a carrier from Wing Commander, multiple ships can enter and exit one at a time into the carrier.
At some point, you have to go from upgrading your ship to replacing it, with various sizes/levels available. e.g. the starter one can only take a small number of small ships, with the one that takes a massive squadron an obscene amount of time taking a fully array of ship sizes with a sizeable quantity of storage.
Whilst a fully upgraded carrier could refuel and repair you, you could only outfit equipment you've brought over. I thought about equipment sharing, but that's a back door to quick money transfer.
I agree with others on the jumps, it shouldn't be something that can rattle around the galaxy - I think they've already said it's on the server tick. Range needs to sit between the top range of a conda and below a megaship.
The ships should deteriorate through use, not through time. That way small squadrons of casual players can still enjoy them without them decaying after a week of inactivity etc. Repairs should be able to be done with mined materials etc., as I imagine some people will up sticks and move their ship to the middle of nowhere to avoid contact with other players.
Whilst themselves they should be safe havens, they should be easily found by other players. So if you decide to sit in your safe haven you can become blockaded by other players reasonably easily (can always get out in private if it's that important to avoid fighting your way out).
There should be something to tie in with crime and punishment. You can't have a hostile force sitting immune in a system (e.g. for power play, or just a PvP base in community goal ganking). There has to be some way for the system authority to remove the ship by force outside of the tick, if it's a source of crime (system type impacting the type of response etc).
I'm not sure, at this point, that they should be used as trading vessels. You can donate stuff to the ship permanently for being used in upgrades, but you can't retrieve them. So no buying out an entire station of stock with one etc. There should be no way to retrieve investments back. They also can't be powerful enough to give a group of organised players an unbreakable advantage over individual commanders (as Elite is all about independent pilots).