In all honesty the way heavy weapons are attached in a battalion or for that matter a company are to the HQ. The formation leader assigns those to his companies/platoons as they see fit. A large part of the COs job is to properly assign those to tasks.
Using a commonwealth WW2 infantry battalion as an example:
The Battalion has an HQ and 4 companies. Each company has a Anti-tank rifle and 2" mortar assigned to the company commander (company HQ). The HQ for the battalion has: an engineer platoon, a carrier recon platoon, an AA platoon and a carrier platoon with mortars directly under it.
It isn't gamey in the slightest to assign these things to the formation HQ. This trend goes up the line as well. The Brigade has 9 AT guns assigned to it...the division HQ has engineers and recon assigned to it. Corps have their own troops in the form of recon, engineering, AA and regular artillery/AT. So is true with Army HQs.
In a battalion you would have all the battalion heavy weapons (more or less) at the finger tips of the battalion commander...even if the TO&E was not quite set up like that, it would happen. The battalion CO is the one who would control those in the end. The Russians in the past at least used to raid their divisions to create Corps level artillery reserves so the Corps commander could assign those to the focus as another example.
Gamey it is not...real militaries function like this. Also having a battalion with 3 line infantry and 1 heavy weapons company is also common as dirt so far as I'm aware.
And this is how I want it to work... I think that if you put artillery units in the Battalion HQ those should automatically be assigned to the individual companies in the combat phase... now I have to set a specific company to do that with.
This means that the best action is to always support ONE company in the battalion to increase the chance of breakthrough...
Say...
Battalion HQ (with medium-bombardment) in Support Line supporting 1st company
1st Company (300 infantry, 30 CAP, 20 LAV) (front-line attack or defence)
2nd/3rd Company (300 infantry, 40 LB) (Front-line defence) both support 1st company
If 1st company take casualties you can take infantry from 2nd/3rd company to reinforce it.
At regiment level you then have one artillery formation to further support one lead company in one battalion, you do the same at division but here you might divide it in three and support the same lead company as you supported in regiment level.
I still would like to have an easy option to force support a formation even if your HQ level is lower rather then attach... you can still do it... you just temporarily attach a bigger HQ to the formation and do the support and then move it back to where it was.
The reason why I had three elements is that they are sort of part of the HQ, they are just there to effectively support the whole company as the game simulate 8h combat rounds and it make very little sense that the battalion HQ only can support one specific company, then you have to reassign this as the combat goes along.
The mechanic feels a bit gamey in that sense.
I probably just think that we should put all support in the HQ just as you suggest and then it automatically support the companies in it.
With light-bombardment weapons we get into even more strange territory as you want one Company with no bombardment and then one with bombardment and one support the other... that is not really how a battalion or companies work. Light-bombardment weapons should support its own company or formation in the bombardment phase, more or less.