Starting about 5 years after First Contact has been made, we could see the rebuilding of Earth after WWIII. The Post-Atomic Horrors, Vulcans guiding humanity, Cochrane working on a new warpdrive, humanity's first gentle steps into outer space, Earth slowly becoming a global community.
I would have zero interest in watching a Trek show like that.
I agree as a total concept I wouldn't watch it, specifically seeing the "Post-Atomic Horrors' on a regular basis would kill the concept all by itself.
However, seeing "humanity's first gentle steps into outer space" likely would hold some level of interest for me, if they could do it in an entertaining way. A show that depicted Humans interacting with far away aliens, visiting alien worlds, They can be traders or non-government explorers (maybe for a private company or organization). Set fifty or seventy years prior to Enterprise and it's "official" first exploration ship.
Babylon Five was only occasional about space exploration, but it was there too. The ship in Firefly only had hand guns, nothing mounted on the ship (except once).
Centered around a ship to the stars, but not a "starship."