All right, I've given it a bit more thought.
Stargate - Futures
Premise: A few SG teams from the present gate 300 years into the future, after humans from Earth have expanded to hundreds of alien worlds and their population is in the trillions.
Making the handful of relic SG team members relevant in a highly populated, advanced future:
Every culture that went through the stargate was steeped in SG mission reports which described their destination, and most first-contacts were made by SGC personnel. To these worlds, SG members are a bit like a blend of the early explorers of North America, the Pilgrims, and the Founding Fathers, giving them a gravitas that future squabbling politicians can never match. Almost all of the planets, whatever their differences with each other or the current core worlds, will meet and hear out what an original SG member has to say. This makes the SG team members natural diplomats and troubleshooters. If not George Washington, they are certainly Miles Standish, Daniel Boone, Lewis and Clark, and Davy Crockett.
The human worlds have largely finished their exploration and expansion phase, and most of them never even really did that. They just saw the videos of new planets and signed up to leave Earth for a known destination that had already been surveyed by SG personnel. Most can't produce anyone who has any experience with alien cultures or technology, or who have been in actual combat against unknown aliens with unknown odds. When faced with something unknown or alien, the SGC people are still the elite SGC people to call, even to the future humans.
With the sudden expansion of humanity, each nation and people breaking free to claim their own planets, borders disappeared, as did border disputes and wars between nation-states, which eliminated the militaries and eventually anyone with any military experience. SG team members are like relics from our more violent past and are among the very few who have the training, discipline, and experience to actually go into certain situations that arise from time to time. They are Judge Dredd.
If more uniqueness is required, posit that most humans, especially those in Earth's core systems, can't travel through the stargate anymore because they enhanced themselves with an alien biomedical nano-technology, one of whose side-effects was that the nanites, and thus their carriers, can't transit through a wormhole. This had been a built-in feature the aliens had added to limit potentially out of control nanites spreading between worlds through the stargate system, and since it took years to manifest, nobody realized that the technology carried a price. They are the magicians who can walk between worlds instead of flying there in ships. (You could even posit that the nanites can't translate through hyperspace, another plague-protection measure from the alien designers)
If few people are traveling through the stargate system, then most people aren't encountering lifestyles and circumstances much different from their own, and the diffusion of new ideas and technologies will have become more limited. Some planets might still be struggling under fairly primitive conditions, while people from very advanced worlds are bathed in luxury and convenience. The more primitive worlds have trouble applying technology to their situations, while visitors from the more advanced worlds normally sent to help have trouble just coping with life on the primitive worlds (They sit and bitch about no restaurants and no internet access). The SG personnel easily bridge the gap. They are the Peace Corps.
Some of the dictatorial countries (like Syria or North Korea) got their own planets and then were vastly more successful in cutting off their people from outside information and influences. The stagnant, oppressive cultures became vastly more so. The SGC personnel, unlike the pampered people of the core worlds, are quite familiar with those types of societies and how to undermine and overthrow them. They fight oppression, they bring revolution.
And most of all, they're the 20th century lens through which we see and judge the future.
I'm not sure if this idea could be at all compatible with my Stargate - Ecosystem idea, which was a way to encounter even more aliens and alien situations, but the Goa'uld could be easily introduced because it's highly plausible that Ba'al wasn't the last Goa'uld, he was just the last one they knew about. In this future, humans are so dominant that the Goa'uld realize they're better off living essentially as vampires; hidden, mythical, and slowly growing, often taking positions of power in what seems from the outside to be an ordinary world. New communities of them could be interesting, with new internal dynamics "We don't have to rule, my brothers, we just have to thrive."
Another obvious recurring theme is human cultures that have trampled all over planets that were supposed to be protected or off limits, everything from illegal mining to thousands of tourists who go to look at the cute little aliens. So often when the team mentions a pristine world they previously visited, one with a fascinating culture or interesting species, they invariably step out of the gate into a cityscape that looks like a Chicago or Miami. (Humans expand and pave over everything).
It seems like this would be a way to lower production costs because you're eliminating most of the wardrobe, props, and special sets, while expanding the number of interactions they could have, and the level of social commentary those interactions could carry. It even sets up more comedic commentary since alien jokes are a harder than jokes about things like a planet of fat kids with slurpies, and planets founded by fanatics of every wacko social trend that's hit Youtube.
Perhaps a good final twist would be that the leader of the teams is still Jack O'Neill, but the Jack O'Neill that had resulted from illegal Asgard cloning experiments, appeared as a kid, and had gone back to school. He should be graduating about now.