The conjecture that very general degree-n hypersurfaces are not covered by rational surfaces

Let $X$ be a very general hypersurface of degree $n$ in ${\bf P}^n$, with $n\geq 5$. A hypersurface $X$ is covered by rational surfaces if a family of rational surfaces in $X$ has union equal to $X$. Non-coverage conjecture. The hypersurface $X$ is not covered by rational surfaces. This conjecture concerns the existence of rational surfaces in Fano hypersurfaces. The source states it as an open question for degree $n$ hypersurfaces with $n\geq 5$.