I gots another one...
The Federation is frickin' HUGE, Ok?
It's considered canon that the max speed a ship can comfortably sustain is 1000c, or a bit under warp 8. This is established both by Voyager's projected journey home and by Sisko when he tries to collapse the wormhole.
The Federation is 8000 light years across. Assuming Sector 001 is more or less in the middle, that means it takes four years to fly to its edge, and eight to cross it completely.
Even in the days of sail, when a trip to the New World was a really big deal, the crossing typically took under 3 months.