Have you tried applying the relativistic rocket equation to that little journey? A generation ship would be a considerably easier engineering problem than a rocket that can constantly accelerate at 1.5g for 10 years
A generation ship is made pointless by technological advance. Why leave in a 1000yr generation ship now when it will only take 25 years to develop one which gets us there in half the time? And why then if another 25 years could cut that time in half again? For that matter, why not wait, say 150 years until a combination anti-matter / interstellar-hydrogen fueled engine that could accelerate at 1g for a decade?
It'd be kinda silly to arrive 1000yr later only to find the system entirely colonized by people from the 'future'.
The point I was trying to make was that while space is really really big place with vast distances, interesting destinations are still very much reachable with slower-than-light travel. Of course that doesn't make reaching those destinations easy, but it's still most likely significantly easier than FTL.