Except testing -- of the one or two bonues we can actually see -- showed no displayed effect from upper-level HQs.
And removing the HQ from say, a Company while leaving the formation under a Battalion (with intact HQ) should logically simply make the Battalion HQ the unit HQ, and apply the Battalion commanders bonuses at full (and the Regimant commander's at one less step remove, etc.)
Finally, HQ units are pretty cheap so there's not a lot of cost and/or mineral savings in having a 'flat' division, while (once stacking HQ bonuses are working correctly) there's no replacement for the lost bonuses. So you can have +20% combat power and a handful of resources, or +26.25% combat power. I sincerely doubt anything you can do with the aforementioned 'handful of resources' is going to make up for the extra 6.25%.