In TOS, the exploration had a purpose: to find out if aliens were threats to the Federation or potential new Federation members, which would strenghten the alliance and push its boundaries outwards (which implicitly makes the core worlds like Earth safer). There was always a sense that Starfleet had a security mission and were not simply exploring for the sake of pure science, although they made a lot of discoveries along the way that would be useful from a pure science perspective.
They also spent a good deal of time on "interior" missions related to threats to Federation outposts, whether they were Klingons, Doomsday Machines, or flying fried eggs, and diplomatic missions (Elaan of Troyius, Journey to Babel, The Trouble with Tribbles) for the benefit of the Federation.
In TNG, you'd often see the pure-science type exploration (scanning a nebula or some other dull activity) taking place at the start of an episode, right before the shit hits the fan and the real story starts. The message was the same as in TOS: whatever pure science they're doing, that's not what the stories are about because they would put the audience to sleep. For a story to work, there has to be an immediate point and a threat. Science doesn't really provide that, but fighting with adversaries - whether it's all out war or something short of that - does.
DS9 was about diplomacy and war, and made no bones about any pure science. All it did was jettison the element that had been nothing but window dressing in TOS and TNG anyway. Being honest about things at long last.
In VOY, pure science made no sense. It would have conflicted with the need to get home. And that raises an interesting point, that some of these so-called explorers should have been happy to have spent their lifetimes exploring the Delta Quadrant and collecting data to eventually deliver to the Federation in a few decades. Isn't that their job? Why the mania to get home, why are they in space to begin with if they turn their noses up at such a great opportunity for exploration?
In ENT, feh, I don't know what they were doing. It was space tourism, not exploration. They never hung around anywhere long enough to "explore," which raises another issue. If you're a scientist and you find a new world, you start a research station and spend the rest of your life there. It would take many lifetimes to explore a WHOLE NEW WORLD!
But if your goal is to make diplomatic contact, you parlay with the natives and then move on. That's really what
Star Trek is about because they behave like soliders and diplomats, always on the move, not like scientists, who stay put. But Archer had no Federation to parlay on behalf of, and Earth didn't seem to be interested in making alliances for the sake of security or trade, so that left nothing but space tourism as a motive.
Star Trek doesn't work without the Federation unless Earth fills the role of the Federation.
The basic problem here is that Star Trek uses the model of exploration on Earth from Columbus' time onwards as its model. But the motive there wasn't science, it was military expansion and trade. Every so often, a Darwin type would hitch a ride with the soldiers and the traders, but the scientists never ran the show, and they didn't run the show on TOS either.
Gene Roddenberry pitched his new series as Wagon Train to the Stars, also known as, Star Trek.
That's even more misleading than the notion of
Star Trek being about exploration, since
Wagon Train was about settlers and
Star Trek never has followed Earth colonists on their journey to a new home, although it did depict colonists as being people who required the security Starfleet provides.
Star Trek is about the cavalry who protects the settlers, but doesn't just follow along after them. They ride out further than the settlers to intercept threats before they arrive on their doorstep.
