The high-dimensional point-line induced matching conjecture

Let $\mathrm{IM}(d,q)$ denote the maximum size of an induced matching in the point-line incidence graph of $\mathbb{F}_q^d$. High-dimensional induced matching conjecture. For every fixed $d\ge 3$,

$$\mathrm{IM}(d,q)=o(q^d)\qquad\text{as }q\to\infty.$$

Beyond the planar case, essentially no nontrivial upper bounds are known for point-line induced matchings in $\mathbb{F}_q^d$ when $d\ge 3$; even a qualitative improvement over the trivial bound $\mathrm{IM}(d,q)\le q^d$ would be significant.