Yes. Good idea.
Heretic !! (Oh wait, I just openly disagreed with the Patron St of AARs I'm doomed !)
More seriously, I do not like mixing artillery into HQ units, as artillery burns through supply and readiness very very quickly, and that prevents the best use of the support, (possible) traffic control, transport sharing that the HQ is there for in the first place. (If the designer has to put a few pieces in an HQ unit, as there's no other place to go, then I do not grumble so much. But schmusching 3 dozen 105s plus 20 or more 155s into the HQ 4th Inf. Div. is a waste. Especially in games with scales 10 km or less.)
Not every formation should have an HQ unit.. sometimes formations are stronger without them. To me, HQ units provide
a) supply boost;
b)support to formation units ("HQ 4th Div supports the attack");
c)transport asset sharing;
d) traffic control;
e)limited command/control (a weak formation with an HQ unit with only 1 command squad and restrictions on replacement makes the whole formation more subject to breakdowns during the game);
and f)chrome (looks pretty, completes the OOB, retains the illusion of a command hierarchy even though we all know differently)
And, HQ units are part and parcel of the whole (internal/army/force/free support) question.
Of course, I'm usually playing WWII and 2.5 - 10km scale. Larger games, or modern or post-modern scenarios, I think, need a different approach to HQ units.