My fleet carrier serves as the mobile fight ops base, obviously. It has about 10K tons of Tritium since I don't go all over the galaxy with it yet. I have about 20 ships on board. It has all of the functions I can fit. The weekly upkeep is about 27m Cr. It has a buffer of 28 years of upkeep. Obviously upkeep isn't an issue, nor is having enough Cr to do anything. For me, it feels more like I have a presence in the system other than being a visitor if my FC is there in the navigation panel.
What do you do with yours? Short of "anything I want" and the obvious role of storing ships, did you have a more specific activity in mind when you purchased a fleet carrier than having a mobile base of flight operations? I know some do some buying and selling, some do some exploring, some do some other things. What is your current FC activity and plans??
Having a carrier is like having your own personal space station, that moves. You can rest, repair, rearm, resupply, keep your ships, mods, cargo, all your 'Stuff' on board, you can turn in your combat bonds, exploration and trade vouchers, albeit paying a premium for the convenience but still. You can buy and sell commodities, salvage, on foot materials. You can stock and sell ships, modules.
While not perfect, and there are a few missing features that would greatly improve them, carriers are pretty good in their current form, now they can be made amazing with some tweaks here and there. But still, I wouldnt want to go back to being without one. My carrier IS my home now. I live off it in the same way people before had a "Home Station", now the carrier is that. And you get to name it, and customize it to an extent.
People have a sense of ownership, hence why there are so many.
In terms of gameplay, they trim alot of the redundant flying you will catch yourself doing. Imagine jumping your carrier to the orbit of the same planet that has the CZ you want to fight in, getting back into the fight is literally only a few seconds away, vs minutes. Or you want to do a HUGE trade run, but instead of jumping the same route 10+ times, you make short hops with your unshielded Type 9, load up the carrier and jump your cargo in a single jump, or jump it FARTHER to another market that you wouldnt have done in the first place because it's too far for your type 9. then you unload, sell and make a bunch of credits in a single hop. Explorers can park their carrier centrally in a region they are planning to chart and explore, knowing the drop off for your map info is always a few jumps away.
I've noticed that I often think of the universe no longer in how far X is to Y. I plot my activity from a distance from my carrier and decide if I want to move it, or just keep it there. Having a carrier allows you to comfortably create a "center of the universe" that belongs to you and thus have control over. And there it gives you some sense of confidence in that when you go to sleep at night, you know your feet are planted on floor rather than hanging out in the black, if that makes sense.
Having a carrier vs not, is the same as doing a road trip in an RV vs a Car. You can live out of an RV, and depending on the model, pretty dang comfortably too, or you can try to live out of your car, which can be done but only if you absolutely have to but is generally the massively inferior experience.