Just visited a System I call my Home, Barnards Star and in that system alone, we have at a guess...50(ish) fleet carriers.
Fleet carriers should not be a single owned entity, but owned and run by a Squadron.
Discuss.
So... what is the problem? No room for your fleet carrier? Or you just don't like seeing all those carriers on the system map?
I am sympathetic to how ugly a bunch of fleet carriers can make the system map. Honestly, there should be an option to filter those out just like there is on the Nav panel.
But switch FCs to Squadron only? No. I have one and it is far too useful for me in managing my fleet of ships and moving them all around the Bubble (or possibly beyond). I've also found the services, and goods (some of which aren't normally sold by stations), of others' fleet carriers to be of benefit as well. No, individuals should be allowed to own these and not be forced to group up and "share."
Also, as a side note, I go to great lengths to park my Fleet carrier away from others - preferably in systems with one or more stars (preferably scoopable) and no planets - and close to wherever I'm going to be active. Makes travel time from a station to my fleet carrier, to switch ships, as quick as jump vs. a long in system cruise. Also keeps my carrier from adding to the clutter of other carriers on the map.
If full fledge MMOs allow guild halls, guilds, etc. to be owned by a single person (even if it requires a few temporary signatures from others to create), I see no reason why Fleet Carriers should be held to higher standard. Further, the closest game to ED right now (in production, not Alpha) is No Man's Sky. That game has let players have their own Fleet Carriers (i.e. Freighters + fleets of frigates) for years now.
In conclusion, if your beef is with the clutter on the system map, I get that. That is the issue that should be addressed, not scaling down carriers to "Squadron Only." Other than that, I'm not sure why else you are complaining and strongly disagree with your position.