If the units are still attached to the HQ under AI control they will stay close to the HQ anyway, as the AI HQ never lets them get very far away.
Any units that you move not attached to the HQ are effectively under command of the On Map Boss, who's command radius usually covers most of the map anyway, or at least as far as the enemy front line for most of the scenario in very large maps.
It would massively increase the load on the On Map Boss playing like this so command delay times would go up anyway.
The only way to play and not keep your HQ's close would be to move all your units individually with all the HQ's sitting on the edge of the map with in situ orders, which would be a ridiculous way to play.
Things would get complicated when you make player groups under a different HQ as code will have to be put in place to allow for this so as not to penalize the player unfairly due to distance from its organic superior.
I believe there would still be a command load penalty for doing this if the new group was not within the organic formation, or overload anyway, thus preventing player exploits of grouping the whole Division under command of a Bn HQ.
The benefit of using the HQ's is the reduction in the On Map Boss's command load.
In order to use the HQ's for this purpose they will need to be close to their subordinates, as any command you give them other than in situ, will require them to close with their subordinates as a requirement of the existing AI.
So to summarize: The game already promotes close cooperation with the HQ's by the nature of the AI.
Exceptions to this would be rare and could be explained by the use of radios or field telephone.
Edit: The most useless HQ would become the Regiment HQ, if everyone was to just concentrate on playing with the Bn HQ's, so there is cause for concern there I guess, as it would be feasible to leave the RHQ with a defend in situ order where it enters the map, then just reattach the Bn's until they are needed again.
It's not how I would choose to play however.