You would not have SP arty in an infantry tank bde nor assign a battery to a Bde, you would consolidate it into Corps or divisional artillery and assign its FOO where needed, but its British so any FOO can call in fires from any unit and at corps level it draws on supply from corps assets.
The RA organizes by regiment with two firing batteries, with 4 gun troops at this point , if you don't you are doubling the number of specialists from the RASC, RAOC RCS needed to support each each firing battery, regiment at this point had 1 Officer an 1 NCO from each of the corps per regiment and again you don't need to allocate the battery to a brigade you allocate the FOO to the formation being supported with one FOO ( and possibly another observing party) being generated by each battery.
Giving a battery per bde doubles the tail requirement without increasing the firepower available.
Again important to remember there is a limitation not just on kit but also on trained personnel and the more new kit you introduce the more you dilute the numbers of trained personnel in the short term at least.
Why don't the RTC concentrate on the the tank brigade as the operational unit and match it with more supporting troops.
And that's why you don't do it. If the Bde is the operational unit then the BDE needs organic supply, bridging, workshop etc units. If you have them fine but even in 1944 when arguably the Western Allies do you keep artillery command centralised as far as possible because that's how you can commit 400 + guns to support an infantry company right now, and then another one in 20 minutes time 10 miles away.
In crude terms the Germans break down their firepower into penny packets to allow those packets to move independently and quickly but that reduces the firepower available to any single packet, The British mass the firepower but make it very flexible so it can act with overwhelming force in rapid succession. But it does mean the army as a whole wont move as fast as often.
This is actually slightly misleading as the other thing the British do is motorise the whole army so when it moves it actually moves very fast its but its power is from the massed fires and ability to destroy the enemy in place. When the British do break through its much more a pursuit than an attempt to achieve decision by maneuver.
The German system works - and is designed to work by surprise against comparatively weak opponents ( weak at the point of contact) which it can achieve because of mobility.
The mechanics of the fall of France really show this and are the exception vs peer opponents. The German breakthrough is 7 mobile divisions vs 2 very low quality French divisions attempting to cover something like 14 km of front. with the Germans also having 2000 aircraft directly in support. Thereafter its really a race on reaction time, the local French division and corps commanders are quite slow the Germans are not ( although note OKH is just as slow as the French) and the Germans are able to defeat local reserves in detail. After that its German forces moving at lets say 25km per day with the French 9th army fully engaged, so reserves have to come after GQG has given orders but it takes 48 hours for GQG to pass orders down to the executive level ( Gamelins testimony) which he can only do once someone tells him what's going on. So the Germans will be 50 km down the pike by the time the order to move goes to French forces. By 14 May ( 48 hours after the start of the attack) Guderian has 2 Pz Div motoring down the Somme in the way are 1 and 2 DCR 4 DCR forming and at least one DMI. They get no orders to do anything until its too late -so the DMI is caught asleep by a German Division it has no idea is in the area, one of the DCR is scattered over 80km when it gets an order to form up and not much else, they then fight a series of scattered company actions vs Panzer regiments etc etc.
Once the pocket is completed any substantial force approaching the perimeter will detected and disrupted by the luftwaffe well before it gets into tank gun range. As happened to Prioux on 22 May at Arras btw.
By 17 May its all over in Reynauds head at least. The BEF gets no orders until 19th and then acts with commendable speed, as indeed do the French units in the north but they are pocketed and the French in particular are living off supplies on hand at the time.
