Consequence of PIT over $\Bbb Z[x_1,\dots,x_n]$ not having efficient algorithm Given $p(x_1,\dots,x_n),q(x_1,\dots,x_n)\in \Bbb Z[x_1,\dots,x_n]$ such that coefficients of $p,q$ are bounded by $B$, does $p\equiv q$ hold?

Schwartz-Zippel lemma applies here since it holds for general fields and $\Bbb Z\subset\Bbb Q$ and there is an efficient randomized algorithm for this problem.

We expect this problem to have efficient derandomization.

What is the consequence if this problem does not have an efficient derandomization?
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!