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?
Why does any bit of Star Trek *have* to be Star Trek? It doesn't, obviously, so I don't know what the point is of even asking that question. The central question of this thread is what we would like to see for the next ST series, and, out of all the potential new ST series I can think of, this idea is very high on the list of ones I would really like to see.
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.
The point of any story is to focus on the parts of it that are actually interesting, which would fairly obviously not be centered on diplomats discussing baseball in between making treaties. There are all kinds of actually interesting (short and long term) stories that could be made about Federation diplomats or merchants or colonists or anything (and non-fed, as well), even within their own specialties - which does not mean you automatically must always contain the story within their specialties just because. You seriously think alien attacks or weird spacial phenomena only ever happen to massive top of the line starships?
Spaced based adventure is not automatically reserved for ships that say 'USS' in their name.
Also, the biggest advantage of this kind of format would be the ability to switch back and forth between different kinds of characters and settings, so those people who just positively hate merchants for whatever weird reason can still tune in to the other episodes which don't center on the merchants.