Like people have noted, there are so many ways of accomplishing the effects in a game like this that the whole concept needs to be carefully considered.
The elder scrolls type learning thing is something I'm very fond of as well, but it behaves in slightly different way and is closer to normal leveling. Therefore it does not give that "notification screen" type of sense of accomplishment that some people seem to be very addicted to. As a compromise multilevel achievements might work where you got a small bonus every so often.
Another way to accomplish the effect is through the crew or ship components. This is again all very fine, but is part of the normal game and probably not satisfactory for people who like achievements. Separate achievements reward you for playing in certain way while you are struggling towards domination of the entire galaxy and can in that sense add another layer, a meta game if you wish. In that sense achievements can be a good thing, again, if done right.
I really have to say that I like how Alex is involving the community.
He has plenty of options to accomplish progression in the game:
-"wealth" (better ship(s), money, weapons, stations?)
-player character
-crew
-reputation/rank among factions
-story missions (if there is a story)
-achievements
The more I think of it, the more I like some form of accomplishment-system for this game. This game has the potential of being one hell of a time sink with the "just a wee bit more"-feeling. On the other hand I really hope that the pace of progression will be slow enough that we will have the joy of getting a new gun for the first ship and eventually being able to upgrade the ship and much later to be able to buy (or loot) another ship etc. Having achievements would allow the pacing to be slow and still give players sense of progression and accomplishment to give the game even more of that "I'll play just to level up/to get that new gun/that new ship/that 'win a fight against 3 enemies with just one ship'-achievement"-kind if feeling.
Sorry for another lengthy post