I think the problem with capital ships is the conflict between maneuverability and collision with other ships as well as with its own fighters when they take off.
If the capital ship steers slowly, it can't drive against smaller ships when turning, but at the same time nerfing its maneuverability and speed makes it boring to use.
There needs to be a middle way.
I'd like to recommend taking a look at Star Trek Starfleet Command for getting an idea of how a pilot/captain should be able to control their capital ship:
It's not so much about their actual speed, but much more about how many things you get to do while maneuvering.
Take AC Black Flag as another reference.
Of course that game is far away from space combat but you're also controlling a vehicle that is slow at maneuvering, yet enjoyable to play.
The Point is that maneuvering becomes less of the actual action and more of a tactical choice.
You have to anticipate the movements of your opponent and choose how to maneuver, to keep your ship in an ideal firing position relative to its target.
You make tactical choices beyond that by deciding wether to use the broad side of your ship for high dps, or to use disruptor weaponry at the front of your ship.
Aside from maneuvering you'll also order fighter drones to attack specific targets as well as manage the energy output of your ship to keep the shields up, guns firing and engines running like you do with smaller ships, just maybe more in-depth.
And with fighter drones I meant remote controlled ships.
That is necessary to protect a carrier while nobody is online.
If only the pilot is online they still need to be able to defend themselves against ships with comparable firepower.
Therefore a carrier should be able to remote-control its fighters through AI as well as through other players.
Why even stuff a human into a tiny ship while you're in the middle of a large scale battle?
It would be far more effective if the pilot stood inside the carrier and remote-controlled the fighter.
If an enemy ship specifically targets player controlled fighters, they won't get to ruin their day entirely, the fighter pilot will be able to switch to another fighter.
A player crewmember would for example use a VR-seat inside the carrier (tactically spoken it should be near the accommodations) to take control over turrets and fighters.
That would also allow outside-combat gameplay for crewmembers.
A carrier needs to be able to supply themselves from nearby stations through small cargo ships.
Those can be player remote-controlled ships aswell.
Carrier wants to jump while supply ship is still active? Captain gets a warning message. If ignored, the supply ship will be left behind and the controls will be cut-off. (why even bother to avoid that programmingwise?)
Another problem that might occur is how to launch a fighter off a rapidly moving carrier.
I believe the answer is simpler than it first appears:
Simply launch a fighter like a projectile.
If it moves fast enough out of the carrier it can't collide with the carrier's hull.
I imagine it to work like a monorail would:
The figher is trapped in a force field that keeps it in the middle of the ramp as it accelerates.
But how do you land a fighter afterwards?
If the carrier is at least halfway maneuverable enough to be fun to play, a figher would more likely crash into the carrier, than land on it.
There is multiple ways to solve this:
A) you can't land until the carrier is brought to a full stop and extends landing pads that get the fighter back into the carrier.
B) you use the force-field rail technology to catch incoming fighters like with a net, then guide it back into the ship.
I'd prefer A.
Money.
A carrier should of course be expensive and a normal player may not be able to purchase one all by themselves without extreme effort.
That adds another topic to the whole story: Guilds
I'd have another couple thousand ideas for how to implement guilds into Elite

angerous but let's keep it short for now:
Players form guilds, guilds make more cash than single players, that cash can be spent for a capital ship or what ever else, depending on their priorities and playstyle.