Well, for starters the show is called Star Trek, not What Earth Might Be Like In The Not Too Distant Future Trek. And if they had done even half a season of characters arguing about whether they should or shouldn't launch, I don't think there would have been a second season; few, if any, fans care about the politics and bureaucracy behind getting Enterprise and her crew into space.
Ahh, but it wasn't called Star Trek -- at least, not at first. It was just "Enterprise" up until partway into season three. I think it coulda been done. Didn't necessarily mean hanging out on Earth. Coulda been lots of space travel -- from Earth to the orbital graving docks, from the Sol system to the Vulcan system, show us some of the local species and their relationships as Earth and their recently-unified Starfleet start to be a more serious player, etc.
--Jonah