Isn't there now some kind of discussion about whether it really was the galaxy's edge?
Well, that depends on how you define "edge." If you're looking at it 2-dimensionally and assume it means the outer rim of the galactic disk, then obviously that would be an implausibly long journey. But the nearest face of the galactic disk, which can just as validly be called an edge because it is a 3-dimensional structure, is more like 5-600 light-years away -- though that's still a substantial journey by modern understandings of Trek cartography and warp velocities.