Yeah ultimately I feel like the best way to use the multiverse concept for the modern audience would be to allow for one superhero "club" per multiverse. Xmen in one universe, FF in another, avengers in a third.
That narratively solves so many problems, lets you cross the streams when you want the big crossovers, but keeps the stories all tidy and separate most of the time. Then its "why don't people freak out at the Fantastic Four?"..... because in their multiverse people are cool with it, but if they went to the Xmen universe everyone would assume they were mutants and start freaking out.