What isn't Star Trek about it? You can show all the exploration, science fiction storylines, Starfleet and the Federation, Colonists, Merchants, Diplomats, Aliens and anything else you think can hold up its own episode(s).
No, what you suggest would be better utilised as a completely different sci fi work of fiction, why does it have to have the Star Trek labelling?
The appeal of classic Trek especially for the casual viewer is that it engages viewers with its space based adventure, no one really wants to see fictional colonists, merchants and diplomats talking about baseball between negotiating peace treaties of fictional planets, that just reeks of self indulgence. Very much what Berman era Trek is guilty of.