Actually a_majoor,
Combining your thoughts with those of pbi, 2B and the USMC Major that 2B was talking about, with some of my own meandering this is what I come up with now.
Your Single Combat Branch (SCB) unit to be formed as I suggested around a Light Infantry/Rifle core of 3-4 companies and Combat Support Company. BUT... whereas I suggested using the LAVs as a basic carrier for the Support Company use a 30 tonne tracked Carrier like the CV90 in its ISC, Mortar and 105/120 mm variants. That weight of vehicle seems to be reasonably RPG proof. Revive the old concept of the Infantry Tank. Slow and Heavily armoured.
The relatively small number of tracked vehicles (20-25) and their weight, coupled with the light companies, potentially motorized would make for a "medium" weight force with effective armoured support that would be relatively easy to deploy.
By contrast the Cavalry function, ranging over long distances rapidly, would still be best done by the LAV and its variants.
Remember our modern MBT is actually a Medium Battle Tank. It was the compromise between the Heavy Infantry Tank which was slow moving and heavily armoured, and the Light Cavalry Tank which was fast moving and supposedly heavily gunned. The Brits and the Israelis came at the MBT from the Heavy side and created the Merkava and Centurion, while the Germans, French and Americans came at it from the Cavalry side and created the Sherman, the AMX30 and Leopard.