According to Blum's speedup theorem, there exist problems with no asymptotically optimal algorithm. Suppose that NP-complete problems had speedup. We know a problem X with asymptotically time complexity of $Ω(n)$. X can be reduced to a certain NP complete problem with quadratic overhead. Because NP-complete problems have Blum's speedup then that means there is an algorithm O with a time complexity of $O(\log n)$. So if we apply the quadratic reduction from X to O then our new algorithm has a time complexity of $O(\log^2 n)$, which contradicts the optimality of X. Then that means NP-complete problems must have asymptotically optimal time complexity.
Is there something wrong with my assumptions? Also, can this kind of problems with speedup be reduced to any complete problem like NP-complete or P-complete problems?