Let's take an inventory of what, exactly, we're talking about, in terms of "A List" monsters:
- Frankenstein's Monster
- The Wolfman
- The Invisible Man
- The Phantom of the Opera
- Doctor Jekyll/Mister Hyde
- The Hunchback of Notre Dame
- The Gill Man (aka the Creature from the Black Lagoon)
More than enough to sustain a whole slew of films, if they're plotted together properly. There are also a ton of "B List" monsters and characters that could be woven in and amongst them, like the Mole People, Maleva the gypsy from the Wolfman, Van Helsing, Doctor Frankenstein, Ygor, Else Frankenstein, the Cult of the Cobra, the Creeper, etc.
One issue that would have to be addressed is the question of what time-period the movies would take place. Dracula and the Monster are immortal, but the other characters certainly aren't. Dracula originally takes place in the early 19th century, while the Creature from the Black Lagoon was set in the 1950's. Some sort of compression of time-frame would be needed, and some sort of "glue" the way S.H.I.E.L.D. binds the MCU together.
It's also something of the inverse of the MCU, since the monsters are the central, and repeating, characters. Heroes can come and go, but the monsters endure.
I picture this without a single overarching "glue", but rather more direct movie-to-movie connections. So there would be van Helsing as protagonist in a couple of Dracula movies, and a Frankenstein origin film followed by a Bride of Frankenstein-inspired story with Dr. Praetorius as protagonist, then Dracula would move over to Frankenstein, trying to force Frankenstein's son to repeat the experiment, introducing Maleva, then a Wolfman origin story set in the same town as Frankenstein, with a lot of the same secondary characters, and then a Dr. Jekyll and Mr. Hyde film with a lab assistant who will later become the Invisible Man, and so forth.
I think if they don't try to rush things, Universal has the potential to really put together an effective shared universe, treating the material seriously and still recalling the heyday of Universal monster movies where mash-ups between monsters were commonplace. Today we call that a shared universe, and if it's done deliberately, setting things up in one film that payoff in another, it can really work.