It sounds nice but then Nomade type players that rely on the big emptieness of space can no longer hide anywhere. A Home Base is already kinda mandatory. With this it would be near totally impossible to play without a Home Base.
Not that i don't see the charm in it. I'm a hunter myself i want to consume every floating block that exists out there. But with this where would the challenge of finding it be?
Fleets need a function just like the give coordinates of your last entered core in the Navigation menu. It's allready a thing in the game code. It should not be to hard to add this option to every fleet you spawn. So not just search last fleet but a search switch on every single fleet you add.