Non-negligible probability of obtaining a prime ideal by random pre-processing

Let $K$ be a number field of degree $d$, with discriminant $\Delta(K)$, and let $I$ be an ideal with an LLL-reduced $\mathbb{Z}$-basis $b_1,b_2,\ldots,b_d$. Set $B=2^d\Delta(K)$, and let $N$ count the coefficient vectors in the box $[-B,B]^d$ for which the associated quotient is a prime ideal:

$$N=\left| \left\{(r_1,r_2,\ldots,r_d)\in\mathbb{Z}^d:\begin{matrix}\forall 1\leq i\leq d,\ -B\leq r_i\leq B,\\ \text{and }(\sum_{i=1}^d r_i b_i)/I\text{ is a prime ideal} \end{matrix}\right\}\right|.$$

Non-negligible-prime-ideal conjecture. The proportion of such coefficient vectors is inverse-polynomial in $d$ and $\log(B)$:

$$\frac{N}{(2B)^d}>\frac{1}{\operatorname{poly}(d,\log(B))}.$$

This would justify reducing the decision principal ideal problem for general ideals to the prime-ideal case, since random pre-processing would produce a prime ideal with non-negligible probability. The source presents this as a conjectural heuristic; no resolution is supplied.