Hang on a second. These "fleet" ships, what makes them "fleet" ones? Do they belong to us, or do we buy them for the fleet, which then loans them to its members?
You may want to listen to the Ship podcast as Al Rivera said that if you leave the fleet, you lose the ship and fleet items as those are tied to that fleet and it seems they do not want a bunch of fleet hoppers jumping in grabbing ships then leaving.
Transwarping to the base and then leaving the system takes you back to where you activated transwarp. Not sure if intentional or bug, but do not like.
I think this is perfect. If I'm missioning off in Cardie space I can visit starbase, and then go back to what I'm doing, not ending un in Eta Frakin'Eridani all the time.
Maybe they could add a button list like at the academy, so you can beam out to
-previous location -or-
-Eta eridani sector space