As of Disney+'s Loki series, Agent Mobius, as portrayed by Owen Wilson, has officially stepped into the Marvel Cinematic Universe. As an agent of the Time Variance Authority, Mobius is crucial to preserving the timestream. While his attention is on the God of Mischief in the MCU, Mobius has spent much more time monitoring the time-traveling misadventures of the Fantastic Four in comics.
Mobius made a brief appearance in 1991's Fantastic Four #352, by Walter Simonson, before making his first full appearance in the following issue. As a high-ranking member of the TVA, Mobius had Justice Peace abduct the Fantastic Four and bring them to the TVA, trying them for crimes against synchronicity.
First and foremost on their list of offenses was voyaging into the Timestream to destroy the Time Bubble. This Time Bubble was meant to wipe out the Fantastic Four's timeline 40 years in the future, but Marvel's First Family changed their intended fate by destroying the bubble.
Behind the scenes, Mobius had previously tried to punish the Fantastic Four for their actions. While traveling across time and space, the Fantastic Four were briefly stuck in the Mesozoic era without their powers, thanks to the TVA. And right before the Fantastic Four's detainment by the TVA, Reed Richards was also engaged in a time-traveling duel with Doctor Doom.
This was the last straw, earning Mobius' undivided attention. Of course, the Fantastic Four eventually devised a plan to escape, with the Human Torch and the Thing distracting the TVA while Reed and the Invisible Woman planted a virus that temporarily erased their timeline from the TVA's records. Mobius still managed to return in 1994's Fantastic Four Annual #27, by Mark Gruenwald and Mike Gustovich. In this issue, the Fantastic Four, including Scott Lang's Ant-Man, managed to help Mobius rise up in the ranks of the TVA.
Marvel's First Family even convinced Mobius that he should try to work for the TVA's rival company, the Kang Dynasty. After telling his superiors of this, Mobius was promoted at the TVA. In 2005's 4 #15, by Roberto Aguirre-Sacasa and Jim Muniz, Mobius reluctantly asked the Fantastic Four for help against temporal anomalies, caused by Ramades, the oft-forgotten son of Kang.
In 2005's She-Hulk #3, by Dan Slott, Juan Bobillo, Paul Pelletier, Rick Magyar, Scott Kolins, Mike Vosburg, Amanda Conner, Jimmy Palmiotti, Ron Frenz, Joe Sinnott, Sal Buscema, Mike Mayhew, Don Simpson, Lee Weeks, Eric Powell, Tom Grummett and Gary Erskine, Mobius presided over She-Hulk's trial as well. Jennifer Walters had tried to warn Hawkeye of his death in "Avengers Disassembled" before it happened, for which the TVA placed her on trial.
Although she's also a regular Avenger, She-Hulk has been a vital member of the Fantastic Four, making this occasion another judgment of Marvel's First Family. It's perfectly understandable that Mobius would carefully monitor the Fantastic Four's activities, considering their importance to the timestream. The instance in which the Fantastic Four destroyed the Time Bubble is only one of the many adventures where they've been active players throughout time and space.
The number of times that the Fantastic Four have repelled Galactus from devouring Earth is astounding, defying the natural order. More importantly, the Fantastic Four were the pioneers of the modern Marvel Universe, ushering in the age of heroes. If the Fantastic Four weren't around, neither would several heroes who have impacted the universe. A particularly important moment came when Mobius offered that, if the Thing stopped his rampage on the TVA, he would make it so that Ben Grimm never became the Thing in the first place.
The implications of this offer are vast, considering that, if Ben never became the Thing, the Fantastic Four wouldn't exist at all. Without the Fantastic Four, several catastrophic universal events would have taken place. Still, the Marvel Universe would be a very different place without the Fantastic Four, which is why Mobius watches them.
The Fantastic Four have shaped the Marvel Universe, ushered in an age of heroes, saved the Earth several times over and explored new frontiers throughout the universe. But tiAgent Mobius, however, the Fantastic Four are some of the biggest wild cards in the timestream.