Conjectured recursion for the ML degree of Grassmannians

For $n\geq4$, let $\operatorname{Gr}_{2,n}\subseteq\mathbb{P}^{\binom{n}{2}-1}$ denote the Grassmannian of lines in $\mathbb{P}^{n-1}$, with homogeneous coordinates $p_{ij}$, and let $\operatorname{MLdegree}(X)$ denote the maximum likelihood degree of a variety $X$. Grassmannian ML-degree recursion. For $n\geq4$,

$$\operatorname{MLdegree}(\operatorname{Gr}_{2,n})=\operatorname{MLdegree}(\operatorname{Gr}_{2,n+1}\cap\{p_{12}=0\}).$$

The conjecture is proposed to motivate a recursive formula for ML degrees of Grassmannians. The source reports computational data for $n=4,5,6$ but gives no proof or resolution.