I’d rather they not be obscenely expensive, mobile war platforms to simply sink credits into endlessly. Expensive, sure, but not the hundreds of billions I've seen more than a few people demanding. That's just silly.
As for any sort of balancing - it seems unlikely these things will be super cruising about anyways. I suspect they will be(have like) other megaships, with largely static positions in systems. Given that their purpose is to haul other ships, not serve as mobile blockades, I don't see a need for them to have any manner of armament at all. It's not like we can blow up megaships in the first place - we can't even blow up Capital Ships.
If they're only usable by those players "assigned" to it, then any other docking requests would simply be denied. No need for loitering fines, and trespassing can be dealt with by the ships aboard or belonging to the carrier.
As for their jump range, I would expect these not to use a standard frame shift jump, but something more like the hyperspace drives of Capital Ships. A destination is selected, and once engaged, it rolls off into the black fog and is gone.
Since this is not, nor should ever become Eve, there's no need for these to be battle platforms, just simple carriers. Sure, they could be used as a staging area for combat fleets, but that's really all they should be doing. They will also need to be available in all modes of play. Though that does raise some interesting questions as well - like how could a Solo commander dock more than one ship on a carrier? Ship transfer seems reasonable enough.
As for what sorts of facilities they would have? Refuel, Rearm, Repair, Shipyard and Livery, but no ships for sale, just transfer and exchange. Outfitting to allow for role-changes, and Helm operations to select and initiate a hyperspace jump.
I also agree, fuel for these should be non-standard. something that would need to be collected by the smaller craft onboard, but shouldn't be annoying either.