There's a reason it's called special relativity. It only works in special cases. Eucludian geometry and Newtonian mechanics are inconsistent, btw. Special relativity solves these inconsistencies in the special contexts where they originally came up (predicting the Lorentz contraction and time dilation which is experimentally observed). It wasn't until the curved space of general relativity was discovered that we had a fully consistent model.
And yes, curved space of general relativity fully explains the rotating disc in a way that is self-consistent in in agreement with observed results (as proven by Gravity Probe B, among other things).
You need GR if you want to treat talk about the rotating reference frame of the disk. Otherwise SR is fine.
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.