Is a quadratic nondeterminism speed-up of deterministic computation plausible? This is a follow up to 
nondeterministic speed-up of deterministic computation.

Is it plausible that nondeterminism (or more generally alternation)
would allow a general quadratic speed-up of deterministic computation?
Or are there any known implausible consequences for something like
 $\mathsf{DTime}(n^2) \subseteq \mathsf{NTime}(n)$?
Note that even a result along the lines of $\mathsf{DTime}(\tilde{O}(n^2)) \subseteq \mathsf{NTime}(n^{2-\epsilon})$ would violate NSETH as univariate polynomial identity testing (as defined in section 3.2) can be solved in $\tilde{O}(n^2)$ time deterministically, but there doesn't seem to be an obvious way to use nondeterminism to help prove identity.