"I will install the anus of the Phantom of the Opera into the hands of a Frankenstein ... FOR SCIENCE."
"Not so!" huffed Hollywood, putting its cigar out in the open eye of a screenwriter. "People wouldn't buy that kind of absurd logic in our stories about the reanimated corpses of Egyptian supergods. We have to create our own secret government organization that gets these guys together." Thus, Project Monarch and Prodigium were born, with little regard for what their actual purposes in the movies would be.
Both organizations are around to keep track of monsters and ... make sure they're cool? Project Monarch appears in Godzilla and Kong: Skull Island, but all we really learn about them in both of those movies is that their members like to stand around while the other characters participate in the plot. They say things like "Let them fight," and while that's a rad line to say while nonchalantly looking off into the distance, who the fuck are you, dude? You haven't helped at all in this whole film, and now you get to be the guy to decide whether or not it's cool for a trio of 400-foot-tall mutants to destroy a major city while they hopefully murder each other?
Warner Bros. Pictures
"Bro, you sound, like, real smart. But just letting them do their thing is how we got into this whole mess."
The same goes for Prodigium, an exposition generator which shows up to be like "Yup, that's definitely a mummy" and then get slaughtered. They suck at their jobs at every turn, but god forbid we find any other way to ensure a monster mash. Even the Amazing Spider-Man series, which had a whole catalog of great Spider-Man villains to use, chose to focus the endgame of the story on some unnamed guy who happened to have the cellphone number of every criminal in town.