That I'll agree with. Not with what follows.
So far okay but not really relevant and I should point out there was a period when a grouping of three or four artillery batteries was called a brigade.
Here's where you lose me. In effect we already have that. Each of the three regular force infantry "regiments" have some fifteen companies (more if you count their reserve force affiliates like the Loyal Eddies, 4th RCR and 4th and 6th R22eR) but that's not what you are suggesting. Your suggestion is more like a bridge between regimentally managing the personnel and mess silver and also taking over the role of the training of the various elements which is currently the job of the CMBGs.
It's a bit like proposing we go back to three battalion (or more) regiments vice brigades or alternatively the regiments just churn out deployable entities which are then assigned to a task force of some type for operational employment. This doesn't make anything better and begs the questions of what role do the brigade headquarters have that form the task forces? They too need training. Do they just train themselves and then get assigned some selection of battalions formed by others? To an extent that too has been tried before with divisions that had brigade headquarters or combat commands which were assigned battalions by the division as required.
Other than grouping cap badges I see no real advantages - and I'm not even sure that this is an advantage. Personally I'm all for breaking up the regimental infantry power blocks and having the corps of infantry built entirely out of single tactical battalion - each with their own unique regimental title - and which battalions can be assigned and shuffled around between tactical brigades and divisions for training and operations as required
I know that you think that these mega regiments can easily spin off regimental (i.e. battalion-sized) headquarters but that just ain't so. It's not like Custer saying "Reno. you take your battalion that way. Benteen. You go that way. And I'll take everyone else and head up this way." The gunners are still working in reestablishing regiments and regimental headquarters and now artillery brigades and brigade headquarters after the great Afghan single-battery battle group debacle. We've literally got a generation of gunners relearning how to do cold war. My guess is the RCAC is in the same shape. Both their equipment holdings are founded on the concept of having just enough crap to generate a single operational sub-unit.
Anyone who thinks of artillery batteries and tank squadrons as Lego pieces doesn't have a solid handle of how you create and use artillery and armoured regiments. It's a systemic problem we need to overcome. We need to think in terms of force generating tactically deployable formations and not sub-units that get cobbled together into . . . something.