I agree skirmish is very flawed, but there are some mistakes in your reasoning here. Basically, your assumption is that there will always be a minimum of 2 cav and 2 archers due to the nature of their classes in a single fight, but this doesn't necessarily hold. As an example, if the proper fight is chosen, it is possible to fight in areas (or times e.g. when opponent is caught moving) when there is no effective crossfire. In this situation, a team with more inf has an advantage, with the 2nd archer being dead weight either in the group fight, or not involved creating a 3v2 (or similar). Another example would be if you managed to position yourself defensively around a single objective, with 3 inf and 2 archers, this would be a nightmare for cav to attack, most likely being dismounted early.
And this is exactly what we saw in 6v6 tournaments in Warband, where eventually on closed maps (the most comparable style to BL maps) the normal set up ended up being 3 inf minimum, with a mix of 2/1 in the support classes (either 1 archer or 1 cav, usually the former).
There are other reasons that the other classes are preferred in skirmish, mostly due to respawns. It becomes less impactful if you catch a 2/2/2 team out of position and kill their archers, if those archers simply respawn and starting shooting you again. Similarly, to take our second example of the 1 cav, being defensive and dismounting 2 enemy cav matters much less when doing so disrupts your whole defense, creating space for the attack, and then the cav simply respawn and return instantly to the fight.
There are also mechanical balance issues regarding the classes themselves e.g. cav much discussed being too strong, and archers being able to bypass shields too often. And finally the melee mechanics themselves are not yet good enough to benefit melee fighting which inherently discourages players from engaging in it, even inf.
TLDR the root of the issue is in the game mode which disproportionally benefits support classes, not the 6v6 numbers.