Existence of a limiting density for primitive roots among polynomial primes

Let $f(X)\in\mathbb Z[X]$ represent infinitely many primes, and let $g\in G$, where $G$ is the set of integers under consideration as possible primitive roots. Define

$$R_g(f;x)=\frac{\#\{p\le x:f(m)=p\text{ for some }m\text{ and }g\text{ is a primitive root modulo }p\}}{\#\{p\le x:f(m)=p\text{ for some }m\}}.$$

Primitive-root density conjecture. The quotient $R_g(f;x)$ tends to a limit as $x$ tends to infinity; denote this conjectural density by $\delta_g(f)$. This predicts that the relative proportion of polynomial prime values for which $g$ is a primitive root exists. The paper presents it as numerical evidence and a heuristic expectation; no proof or resolution is supplied.