TBH, I rarely have much directly attached to the highest level HQ - the depot, possibly a small artillery reserve and an AT detachment. Most of the rest is deployed forward under it's own commander with orders in progress. I only regroup units to their higher HQ for administrative movements, or to relieve command load in static and non-active portions of the front.
Not that I don't use major formations for operations sometimes - I have launched Divisional attacks on occasion, though it is usually Regt/Bn with mutual support by presence/coordination.
Regt HQ is usually: The HQ, The base if not grouped into a rear-area-support-group, or moving to intimate support range, infantry artillery not actively supporting a line Bn... which is agile enough to displace without huge problems to subordinates.
Divisional HQ usually has a few more supports, as I keep the reserves and group Regt support etc here... or under a rear HQ under this level command... but it also doesn't need to displace quite so often... and it should be a big deal when you do. It sometimes took days to sort out after an HQ movement, and usually hours at least.
An obvious point is that maybe HQ shouldn't be on the enemy 'Rollbahn' - major arteries and towns are great and all, but that large village on the B Road 3 miles away might be a lot safer... and the rough ground & woods in the valley behind might be safer still, although less easy to work in. Supply is more tied to the road network but again a crossroads on two major routes might not be the wisest choice... too obvious and too risky if there is a collapse of the front and mechanised penetration.
Artillery is more capable of self-protection, so it can be used for area-denial quite usefully, just avoid long-range site lines if he has any sort of CB potential.