Well, now, I disagree with this. I think there’s a rich enough history and a complex enough world that a creative individual can come up with all sorts of ways to spin the material and make it fresh.
For example, along the lines of what athelas mentions regarding JMS’s rumored fall-of-Federation premise, I’ve been mulling a possible angle for a new Trek series. I came up with this very early in Enterprise’s run, when I was trying to figure out why the new show wasn’t working. My plan was to work up a detailed proposal, more a wish list than fan fic, and basically spam all the Trek boards with it to see if people agreed with me and if so try to drum up general interest.
In my hypothetical new series, a strange and powerful force invades the Federation, penetrating from the least-known quadrant of the galaxy. This enemy wreaks total havoc, destroying thousands of worlds and wrecking the political structure. A last-ditch effort eliminates the threat, but not until the Federation has been almost completely wiped out, leaving scattered remnants and isolated communities throughout known space. This all happens at the beginning of the pilot; it’s just setup.
The actual series would center on the rebuilding effort. We would have a civilian ship with a political and diplomatic corps, paired with a hardass military vessel, accompanying one another as they travel from one enclave of survivors to the next, taking stock, and trying to recruit them into re-forming the government or something like it. The story would be about the tension between the two sides, the military and the civilian, and how they balance the leadership roles in a tense and dangerous environment. Instead of focusing on a single captain, loyalties would be divided between the military leader and the political leader, unified only by their belief that trying to rebuild something like they had before is the right thing to do. The story would also include resistance from some worlds and groups of worlds who show no interest in rejoining the Federation Redux, either because they felt abandoned during the invasion or even neglected beforehand, and the ethics of trying to manipulate people into doing something against their short-term interest with a view toward the long-term success of a wider civilization. Further, there would be conflict between our primary group and other groups they encounter who claim themselves to be the legitimate heirs to the Federation, and who want to rebuild according to their own beliefs about what civilization should be. I have a lot more detail about the premise, because I’ve been thinking about it for a while, but that’s the idea in a nutshell.
I think this has a lot of potential. There’s room for both standalone episodes (introducing a situation and resolving it in an hour) and long arcs (as the various factions begin to form and clash). Because the conflicts are primarily human, about what people do and don’t want to do, you don’t waste time on ridiculous SF nonsense about time travel and sentient black holes and whatever other crap the writers dream up between bong hits. The technology goes to the background, in other words.
And best of all, the show becomes relevant again. The original Kirk-era Trek was relevant because it was a veiled look at the modern world; they could treat issues and themes that connected with viewers’ lives by transplanting our concerns into an analogous-but-metaphorical SF context. That is, after all, what good SF is supposed to be, right? It isn’t about aliens and teleporters and 2320’s style death rays. It’s about us, or at least it should be. By taking a hard look at what Federation society had become, and letting the characters wade through the mess of deciding what of that accumulated but lost culture they thought was important and wanted to recapture, and setting them against other people who have different priorities, you get to talk about what we in modern society are wrestling with as we try to figure out what compromises we need to make to remain safe and secure in an ever-more-complex and dangerous world.
I called it Star Trek: Wayfarer, and I was really proud of my concept.
But then Battlestar Galactica came along and announced with its first few hours that it would be doing probably 90% of what I wanted to do with the new Trek, and better than I was going to do it, so… yeah. 
Anyway, the point is, I don’t agree that the world is played out. I think, with a willingness to go back to the drawing board and take some creative chances, there’s lots of stuff you could do with the Trekverse that would be new, interesting, and exciting. But I also think that the current creative team is playing defense, not taking any risks because they’re trying to protect the profitability of the existing franchise instead of striking out in new directions and expanding the world’s storytelling potential. And because of that, I reluctantly conclude that a break is required to allow the people in charge to clean house.
Basically, as much as we all complain about the Big Reset Button, that’s what the artistic staff needs. They haven’t rethought themselves in years, and they’re so laden with baggage they’ve lost their creative dexterity. Everyone needs to step back and think about what Trek is, its strengths (a rational worldview, a sense of optimism) and its weaknesses (a preoccupation with technology at the expense of the characters’ humanity), and go forward on that basis.
It can be done. It just requires the will to do it.