Consequence of PIT over $\Bbb Z[x_1,\dots,x_n]$ not having efficient algorithm
Since PIT is in $\mathsf{coRP}$, if there is no efficient derandomization then $\mathsf{P} \neq \mathsf{RP}$ (and, in particular, $\mathsf{P} \neq \mathsf{NP}$, but that's not so surprising, since we expect that to be true anyways). This also implies, of course, that $\mathsf{P} \neq \mathsf{BPP}$, so anything which implies $\mathsf{P} = \mathsf{BPP}$ becomes false. For example, sufficiently strong pseudorandom number generators do not exist, and $\mathsf{E} = \mathsf{DTIME}(2^{O(n)})$ would have subexponential size circuits!