Most people who like the '60s setting idea are those who think the team doesn't work in the modern era. The reason they seem to think that is because their movies haven't really worked. But we haven't seen them given a movie that really draws on the charm and Lee/Kirby energy, they haven't really been given a chance yet. The 2005 movie was probably the closest, because it seemed to get the Ben/Johnny chemistry right. But that's just half the team, plus they ruined Dr. Doom.
I see no reason why the FF shouldn't work in the present time. If you put them in the '60s, then they can't really interact with the rest of the Marvel Universe. Sounds like they may plan to put their origin in the '60s, then strand them in the quantum universe, where they don't age, giving them a kind of Captain America "heroes out of time" vibe that they were never meant to have.
The only thing I see that accomplishing is establishing them as an earlier superhero team than the Avengers, but they would still presumably be predated by the Invaders, if that ever becomes a thing.