As previously mentioned, joining someone else's squadron doesn't get YOU a Carrier. At best, you can hitch a ride on someone else's (unless you are one of the very few who get to be the leader of a popular squadron).
But I think FDev are storing up a problem for the future, unless something changes. You currently can't be a member of more than one squadron, and once a squadron has declared its allegiance (to a superpower, a PP power, and/or a minor faction), this can never be changed. So if a squadron is set up to advance the Purple Pangolins of Procyon or whatever, and gets a Carrier, that is what the Carrier is for. And this will NEVER change. At present, you can at least disband a squadron and start agein, but in future this will mean losing the Carrier.
So, just how much of a fan of the Purple Pangolins are you? Enough to commit yourself to building their Carrier and then supporting them indefinitely? When enough people get a bit tired of relentlessly supporting the Purple Pangolins and decide to move on to other causes... then what?
That is the problem right there isn't it?
Everybody wants to own their own carrier. LOL.
Even though it requires a team of players to actually operate one.
So hilarious. Everybody wants to be the Indian Chief.