It would help if there was an indicator that showed up when people bought their first (and second and maybe third) destroyer, cruiser or capital ship, defeated some dangerous bounty for the first time, colonised a planet, had a colony reach size whatever, et cetera. I am good at the game and to me, restarting a game to try something different or to obtain a particular ship is easy, because Starsector itself is rather easy to me and making a new run involves no sacrifices. People other than me, though, might get attached to a particular ship, or spend enough time in a run they don't want to throw away their progress and long for a way to transfer their progress, as that's the only way they'll enjoy new non-early game content in a reasonable amount of time. With some progress indicators, it would be easier to decide if people are just lazy, or are they onto something.
I personally would rather settle on a compromise, where accomplishing certain things gets you fast start tokens, that can give you a random or a predetermined advantage upon the start of a new game. Progress wouldn't be completely lost, without (hopefully) undermining the regular game design too much. That would be a nice achievement system. I wonder, though, if whatever Alex is cooking up in the 0.10 update is going to change this perception...