Special Relativity + some basic mechanics leads to an apparent contradiction in the expected measurements, which is only resolved by introducing a curved space(time). So this would be a failure of self-consistency: the same theory leads to two different results for the same experiment.
However, the two measurements of ostensibly the same thing are done by different observers, so there is no requirement that they should agree. Introducing curved space for the rotating disk shows how to calculate distances consistently.
which is only resolved by introducing a curved space(time).
The spacetime itself is flat (if the mass of the pie is negligible), but the spacelike slices are curved because you're slicing it in a weird way.
As per a recent comment this thread is meant to voice contrarian opinions, that is anything this community tends not to agree with. Thus I ask you to post your contrarian views and upvote anything you do not agree with based on personal beliefs. Spam and trolling still needs to be downvoted.