Why? “To explore strange, new worlds. To seek out new life and new civilizations…” You can do that in any century
That's kind of the point. Time/Dates in Star Trek are, for all intents and purposes, completely arbitrary. So why not the franchise live in the 'era' with the most familiar iconography?
And then there is there's
Dennis's point that there is really nothing left to explore in the 25th century. The issue with Berman-era Trek is it abandoned the pretense of the vastness of the Milky Way and started drawing lines on the map and began to heavily favor the
Geo-political over the unknown to the point where "strange new worlds" became a misnomer. And, yes, even Voyager fell into this trap.
The quadrants became analogs for contents. "70,000 Light Years" became shorthand for "across the ocean" -- the characters could be anywhere within Gamma or Delta and yet always be 70,000 lightyears from Earth.
The problem with this is it greatly shrinks the perceived breadth of the Star Trek 'universe' to the point where, by the end of the TNG era, the whole thing is nicely charted out. Certainly, from a purely 'realistic' standpoint, there's still all but infinite stars left to explore. But that's not how the franchise chose to present it -- and clearly both Disco and Picard have both continued to do so.
And if they were to continue into the 25th century they would undoubtedly focus solely on the politics. And there is a very significant group of people with whom that would be fine. After all, as a general rule, fan creations (fics, films, whatever) tend to focus on the politics. So there is an interest in it. But the outside that group the level interest declines rapidly. And to Josephine Public, it doesn't exist at all. And if they were to do any kind of 'exploration', it would have to be limited to mostly Voyageresque spacial anomalies whilst croutoning the salmagundi array and sauteeing the Mirepoix Effect with the very occasional visits to the Tolkians, the Hippi, the Bug'Atti, and the V'eyron. And no one wants that again.