But why did I write that it is the
exception that proves the rule? So here's the thing- first, unlike more mainstream IPs like Marvel, Star Wars, and Star Trek, Cthulhu and the Lovecraftian universe wasn't very
character driven. It was always more of a genre- cosmic horror.
Leaving aside genre elements for a moment, I think that from a standpoint of...I don't want to say "branding" or "intellectual property," because those are more marketing/legal concerns than anything else; perhaps "recognition" is the better term...the Cthulhu Mythos has something that a lot of other series (for lack of a better term) lack, which is an iconic antagonist (who leads a suite of antagonists) that aren't bound up to any particular narrative, aren't tied to any particular hero, and have no canonical defeat.
For a lot of licensed properties, the stories involved are what drives them, and those stories are often intrinsically tied to the characters. To that end, we know that a lot of PCs don't like to be tied down to the idea of playing an established character; in my experience, most see it as a straitjacket that infringes on how they'd
prefer to play (even as they ruthlessly exploit those characters' abilities). But villains are characters that the heroes love to struggle against, often even when they should be rightfully scared of them. Put Darth Vader in your Star Wars game and, if the players aren't properly intimidated, they'll start dreaming up all sorts of creative ways to manipulate the game rules in order to bump him off. Everyone wants that badge of honor on their character sheet.
Naturally, that can be a bit of a problem for the GM, since it disrupts the established narrative to the point of turning the setting into a mess, leaving them floundering to put things back together and figure out what happens next. For many GMs, this is the reason to keep the PCs far away from the rebellion, either in terms of setting them on the Outer Rim, in the past or future, etc.
Cthulhu doesn't have that problem. Not only is there no established narrative beyond a few short stories, but the villain isn't anyone they can ever truly fight (at least, not fight and win; Cthulhu eats 1d4 investigators each turn). There's minions aplenty to foil, but you can't kill Cthulhu, and there's no heroic narrative that says otherwise. As such, Cthulhu becomes an enduring symbol for the entire franchise, a Sauron with no One Ring to tear him down. It allows the limits of an established IP to be transcended, because there's no hard-and-fast narrative to set the framework.
Of course, that works against establishing such an IP in terms of "Disneyfication" as well. There've been plenty of Cthulhu-themed movies and TV series, but none that have truly put the Mythos front-and-center while
also becoming an enduring staple of popular culture (i.e. to the point of being a media universe in-and-of themselves). Though it would have been interesting if Universal's Monster Universe (or whatever it was going to be called) could have pulled this off.
All of which goes back to the point in the OP, which is that what makes an engaging bit of media fiction, and particularly an entire media universe, doesn't necessarily lend itself to a very good tabletop role-playing game.