Does iron(VI) fluoride exist?
Besides steric factors related to the small size of the transition metal core, we could be seeing an electronic effect described in this answer.  Iron is fairly early in the transition metal series, so when pushed beyond the $+3$ oxidation state it has few $d$ electrons in the central core.  As explained in the referenced answer, this makes the iron strongly pi-electron accepting, and therefore more favorable for combining with a stronger pi-donor ligand such as oxide instead of fluoride.