When I watched the movie, I immediatly thought about the FF, as soon as the beginning ... at the same time, I also thought that making a new FF live movie with an excellent story is getting harder & harder.
Most of the Marvel cosmic characters already appeared in Guardians of the Galaxy (even the Watchers !). Even though Galactus & Silver Surfer couldn't appear, Ego & Star-Lord replaced them as the Anti-Galactus (Ego was created as the antithesis of Galactus) and the Anti-Surfer (Peter Quill is the reverse of Norrin Radd).
Black Panther is already introduced.
The Skrulls will appear in Captain Marvel.
There has been a failed attempt about an Inhumans TV series.
One of the key aspects of the FF was meeting all these iconic characters. They were part of the natural environment of the comic book. If Marvel has already used them, what is left for the FF to discover ?
In my opinion, the FF can only be introduced as a spacetime paradox (similar in some way to Sentry) : the world's greatest superhero team that everybody forgot because they were removed from the spacetime continuity of the MCU's reality.
It is at the same time a meta-message to the fans and the perfect way to introduce them to the MCU's reality.
I don't think the X-Men should be introduced in the MCU (they could be left in their own timeline) but the FF are closer to the MCU's characters than the X-Men.
Spacetime travel has always been part of the DNA of the book (both Doom & Rama-Tut are time travellers) and Reed's experiments to travel to the Negative Zone were part of a bigger plan to discover all the Multiverse.
In the MCU, it will be revealed that they were the forgotten superhero team of the Space Age.
In the 1960s, Reed was the founder of the FF team and also the managing director of the Future Foundation, a brain-trust located in the Baxter Building.
He would also have been an "Illuminati" (the others being Howard Stark, Hank Pym, T'Chaka and, perhaps, the Ancient One and even Namor if the legal problems about the rights of the character are truly resolved).
Perhaps, the FF asked the Ancient One to use the Time Infinity Stone to remove them from reality to prevent a cosmic event from occurring.
Maybe, a battle against the FF on one side and Doom, Kang/Rama-Tut & Annihilus on the other side opened a portal between the MCU's reality and the Negative Zone and the only way to stop a massive matter/antimatter annihilation was to removed the protagonists from the timeline.
... but Infinity War changed everything and the FF (and 3 of their main antagonists) are back.
That's one of the ways I can thing about to save the FF's concept.
The Original Fantastic Four in the 1960s went into space to beat the Russians and the Chinese who were also using Warp drive to figure out what the space Anomally by Jupiter was. They make it there, nearly beating out the Russians (The Red Ghost) and the Chinese crews. The Space Anomally is humanoid and blasts the ships. The Silver Object is heading towards Earth and the ships follow in pursuit, eventually getting caught in the cosmic wake that irradiates both ships.
They crash to Earth, 50 years later. The FF have these super powers and abilities, but they also have this mindset that it is only 1967. They're anomallies in this new world, trying to cope with their new celebrity as well as all this space debris they dragged with them to earth that is irradiating the population and creating monsters in different parts of the globe.
Their mission is to capture and study these anomallies, while also trying to find the "silver bullet" that brought them to Earth. What they don't know is that it is Dr. Doom who has the Silver surfer and who is also trying to drain the power from the Silver Surfer.