I think THE X-FILES has value as a brand, but in the same way MISSION: IMPOSSIBLE had value in 1996. It was just the name. The MISSION: IMPOSSIBLE movies are summer action blockbusters; they make small nods to the heists, mindgames and deceptions of the TV show, but the centerpieces are always Tom Cruise and heights. For better or worse, M:I's value was in its name recognition as opposed to the content. THE X-FILES is a name. I could see it being rebooted as a 21st century revitalization of the source material like SHERLOCK; I could also see it becoming a star vehicle for Alison Brie for movie after movie in which she fights CG aliens with everyday objects.
As for payoffs -- I think BUFFY had the right formula: each season has its own myth-arc. I think SUPERNATURAL has the right attitude: complete your myth-arc as planned even if you get renewed after your conclusion. Come up with a subsequent story instead of stretching out your first one. ANGEL had a neat approach where each season tweaked the premise slightly with new characters and new locations.
I think the most interesting challenge in THE X-FILES for a new creator is also its central weakness: the show is decidedly indecisive on whether its universe operates on scientific principles or supernatural principles. The advanced biotechnology of the Colonists has always been an odd fit next to the vampires, angels, demons and evil dolls. Mulder and Scully never comment on this discrepancy; the magical elements of the X-FILES never confront the technological aspects. It's a symptom of Chris Carter treating each episode like its own XF universe.
I think a rebooted X-FILES should confront this head on. Summer Glau’s Mulder and Rupert Grint Scully find themselves going back and forth between the magical and the technological and try to reconcile how they exist. Are the vampires a form of genetic engineering? Are the ghosts the result of telepathic ability? Why doesn't their world operate on consistent principles? Is it the result of some interference in the very nature of reality? Are the aliens from other planets or from an alternate plane of reality? Has some cataclysm corrupted the laws of nature, bending them and twisting them? Is there a person or an organization causing this? What is their endgame?
And this also gives a reboot room to maneuver. At some point, the skeptic has to move towards believing, so what if it becomes a conflict between Grint believing in the magic, Glau believing in the science, and neither ever being entirely right?
Going with the SHERLOCKesque approach of treating the source material with reverence while moving forward in time --
Season 1: Starting with basics: monsters of the week, an alien conspiracy that's infiltrated the government, Mulder and Scully investigating, occasionally aided by the Lone Gunmen. In the season finale, they encounter David Duchovny's Fox Mulder and help him find his way back to his home dimension.
Season 2: The Lone Gunmen join the FBI as consultants and become regulars.
Season 3: Mulder, Scully and the Gunmen are fired from the FBI, decide to restart the Lone Gunmen magazine and rename it X-Files Magazine.
Season 4: The magazine was so successful in Season 3 that with Season 4, they hire more staff, more trainees and the X-Files has gone from Mulder and Scully in the basement to an underground magazine to a global operation.
Season 5: The alien invasion begins and we have a full season of myth-arc intrigue. The arc is resolved in a feature film where the invasion is thwarted by alien technology used to shift planet Earth out of phase from the aliens' dimension, preventing any further extraterrestrial incursion. The X-Files disbands, having served its purpose and proven the existence of aliens.
The entire operation is bought up by the Department of Defense and Mulder asks Scully to marry her. As Mulder and Scully embrace in their house surrounded by their friends and family, we pan away to see William B. Davis' Smoking Man observing the scene...
Season 6: Mulder and Scully are called out of retirement when a new conspiracy arises, one based in magic rather than technology, and the X-Files Division is reopened as a DOD operation.
Season 7: Mulder and Scully are now being hunted by the Smoking Man's monsters and seek help from the Duchovny and Anderson incarnations of their characters from the parallel universe where the Smoking Man originated. We spend a season with David Duchovny, Gillian Anderson, Summer Glau and Rupert Grint wandering across America, finding monsters of the week.
(Gillian: "I did not want to come back, but my daughter said she'd never forgive me for turning down a chance to work with Ron Weasley.")
Season 8: The Mulders are transformed into vampires by the Smoking Man and the Scullys must find them and cure them before it's too late. (Gillian: "I didn't want to come back, but the chance to stab David Duchovny through the heart was too good to pass up even if he comes back to life after.")
Season 9: With aliens re-entering this reality and the monsters on the loose, the Mulders and Scullys begin a search for the creator of their existence, a mysterious being known only as God. The season ends with the Mulders and Scullys confronting God. God is played by Chris Carter. (Gillian: "I didn't want to come back, but I couldn't turn down the chance to punch Chris Carter in the face.")
Season 10: Carter resolves the multiversal conflict, but at a great cost: the Mulders are trapped in the Glau/Grint universe of monsters and magic and the Scullys are trapped in the Duchovny/Anderson universe of sci-fi aliens. We alternate universes each week as the Mulders and Scullys try to solve cases of the week and find their way home. (Gillian Anderson: "I didn't want to come back, but Rupert Grint said he'd star in an adaptation of my EARTHEND novels if I did.")
Season 11: With the Mulders and Scullys having been restored to the correct universes, Glau and Grint decide they're not ready to stop exploring yet and begin exploring parallel universes. Every week, they visit the universe of a TV show that ended on a cliffhanger and resolve that cliffhanger, so we finally get conclusions to SLIDERS, SARAH CONNOR, PUSHING DAISIES, MY SO CALLED LIFE, FREAKS AND GEEKS, LOIS AND CLARK, QUANTUM LEAP and HEROES and we also find out what happened with Big Eddie in Season 1 of FRINGE and get Walter back to the present day to be reunited with Peter and Olivia.