RDC+ lower-density conjecture for rank-zero elliptic curves

Let $\mathscr{E}$ be the set of isomorphism classes of elliptic curves over ${\mathbb Q}$, ordered by height, and let $\mathscr{E}'$ be the subset consisting of rank-zero elliptic curves with good reduction at $2$ and $3$. For a subset $\mathcal{S}\subset\mathscr{E}$, write $\mathcal{S}(x)$ for the curves in $\mathcal{S}$ of height less than $x$. RDC+ conjecture. The lower density of $\mathscr{E}'$ is

$$\liminf_{x\rightarrow\infty}\frac{\#\mathscr{E}'(x)}{\#\mathscr{E}(x)}=\frac{1}{2}\left(1-\frac{1}{2}\right)\left(1-\frac{1}{3}\right)=\frac{1}{6}.$$

This combines the expected $50\%$ rank-zero proportion with the local proportions of good reduction at $2$ and $3$. The source presents it as a reasonable conjecture and gives no resolution.