The reasons behind a Earth-based show not working are pretty obvious. We know everybody. We know the Romulans, we know the Klingons, we know the Cardassians, we know the Vulcans, we know the Breen and so on and so on.
Ah but do we really? We got to know the Andorians much better during Enterprise than we did in any other Trek shows.
We've seen very little of the other species that make up the Federation there is a lot of stuff we dont know, lots of alliances, old grudges, species who have had disagreements in the past.
It's potentially a very rich canvas to tell intriguing stories.