This is part of balance; if irregulars was resistent to arrows like more expensive infantry this will be a unbalance the game, of course you mean let me purchase the armour as upgrade, but at this point is not better take directly the militia swordmen? I did frequently armies like you describe powerful cavalry and mass of irregulars infantry. Usually the best tactics is (assuming you has the cavalry superiority) use your infantry as target (set it in open mode) and hit his arrows with your arrows. At the end it will be forced to make a choice between it infantry or your arrows. At the end your infantry is so big in number that he cannot make too hard damage if your shooters press his ones.
I can assure you a big mass of irregulars on three lines in compact formation with a general in the middle is very hard to defeat if you has not a strong superiority in shooters.
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