I don't think your analogy holds up. Pikemen are counters to knights. You say that APC's are MBT protection vs RPG' and gunships. That would not be a hard counter... although the rest of your post is a good argument for making MI no more powerful than infantry - just faster.
What I wanted to point out is that a M2 Bradley has hardly any chance in a duel vs. a M1 Abrams, although the M2 carries two TOW anti-tank missiles, which is above average for an IFV. Still, the Bradley has to stand still from the moment the system starts to unfold (it needs some time to be ready for launch) until the missile hits (it is wire-guided and needs signals from the launcher). The main gun of the M1 is gyro-stabilized and can be fired while moving. And most APC have no AT weapon at all, it is considered unneccessary since an APC should never duel a MBT.
So usually an IFV/APC/Mech Inf Unit has very little chance against a MBT in open terrain. If the IFV can hide in a forest and the crew can attack the MBT with shoulder-launched AT missiles, the situation is very different again. The same applies to urban warfare, where the IFV crew can check buildings for attackers, while the MBT is more easily ambushed.
Note that the term "mechanized infantry" clearly means vehicles like the M2 Bradley and its crew. The more general term is "mobilized infantry", which includes infantry transported by unprotected trucks.
I'd say the roles for certain troop types was like this during the cold war:
- MBT's were meant to fight other MBT's.
- MBT's were primarily countered by tank destroyers ("self-propelled AT gun") and gunships
- infantry fighting tanks were rather considered a cheap fallback solution
- IFV's and other infantry added versatility to the MBT's, but they were never meant to fight enemy MBT's
In assymetric conflicts like Iraq the roles shift a bit, since the enemies have only shoulder-launched missiles, traps and mines to fight armoured vehicles.
Translating this into game rules, I'd suggest:
- MBT's and Mech Inf should be equally mobile.
- Reduced sight, city attack penalty, no terrain bonus and move after attack are justified for MBT's.
- Tanks should win very often vs. Mech Inf in open terrain, and still have a slight edge over them when they defend in rough terrain.
- The justification for APC's should be their ressourcelessness, their price and their versatility (no penalties!). They should especially be strong when attacking cities.
- Overall, a combined arms force should be the best strategy in modern combat.