Griffin's dream for primitive roots in polynomial prime values

Let $f$ be a polynomial representing infinitely many distinct primes, let $g\in G$, and let $c_g(f)$ denote the number of primes represented by $f$ for which $g$ is a primitive root, as defined in the paper. Griffin's dream conjecture. (1) For quadratic $f$, Griffin's dream cannot be realized, that is, $c_g(f)<\infty$. (2) For every integer $m\ge1$ and every $g\in G$, there exists a polynomial $f$ such that $c_g(f)>m$. The two assertions contrast an obstruction to having the primitive-root property for all prime values of a quadratic polynomial with the existence of arbitrarily long finite examples; the paper gives them as concluding conjectural claims, with no resolution supplied.