Because Lovecraft's stories don't emphasize spectacle and fiery destruction like most kaiju properties. They emphasize fear of the unknown, of the things that might lurk in the hidden corners of the universe. His stories are slowly paced, mysterious, often dream-like, quiet and subdued up until the climax. Cthulhu isn't a buff omnipotent kaiju with an octopus for a head that eats nuclear bombs for breakfast and makes people go insane when they see him; he's an ancient, unknowable alien thing that's powerful, but still very much mortal.
The closest the Godzilla series has come to a Lovecraftian story is not The Planet Eater. It's Rodan. Or rather, it's the first half of Rodan.
The mystery, the slow escalation of horror as more discoveries are made, the gradual pace building up to the final reveal of Rodan hatching. THAT is what Lovecraft is about, not omnipotent space monsters that eat planets.
The reason Cthulhu vs Godzilla wouldn't work is the very same reason why Rodan stops being a Lovecraftain-style story after the first half. After the reveal of the baby Rodan, it switches gears into becoming a typical disaster movie. Anything Lovecraftian about the movie flies right out the window, never to be seen again, because Lovecraft isn't about spectacle.
And Cthulhu vs Godzilla, like any versus movie, is spectacle.