In reality, the earth would eventually be ripped apart if it were spun faster and faster. At some point, objects on the surface would be moving at orbital velocity, and then things go nuts.
Btw, rigid bodies are not compatible with causality even in principle.
There is some interesting work in what would happen if you tried to spin up a black hole. All evidence indicates that there is a limit to the angular momentum it can have no matter what you do.
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