Good postulation conjecture for general codimension 2 linear subspaces

Let $Y$ be a finite union of general codimension $2$ linear subspaces in projective space $\mathbb P^N$. It has good postulation when, for every integer $d\geqslant 1$, the restriction map

$$H^0(\mathbb P^N,\mathcal O_{\mathbb P^N}(d))\to H^0(Y,\mathcal O_Y(d))$$

has maximal rank.

Good postulation conjecture. A finite union of general codimension $2$ linear subspaces in $\mathbb P^N$ has good postulation.

Good postulation means that the subscheme imposes the expected number of conditions on forms of every degree. The conjecture is motivated by the known result of Hartshorne and Hirschowitz for general lines in projective spaces, while the codimension $2$ case is proposed as a setting for extending that result via specialization to a hyperplane.