Basically I tried to find a weapon combination players (and therefore regular AI empires) have access to that beats shields but is countered by armor.
The contention isn't that it "beats shields", AI trash doesn't beat anything, just that it is
worse against armour and so if you use high armour designs you take less casualties and can beat larger opposing fleets.
Also, the AI has a group of relatively fixed layouts it uses. It will always use energy torpedo corvettes as soon as it unlocks them (no AP), it has two destroyer designs of which is is much more likely to use the one with all PD modules, six cruiser designs, and about five battleship designs one of which is super rare. Against those designs, armour is better.
As a reference, the energy preference AI's most common cruiser design once it has reached the end of the tech tree is 1 Large Plasma, 2 Medium Disruptor, 1 Medium Laser, and one Whirlwind Missile. That means that four out of its five weapons are strongly countered by armour. And none of its other designs are much better, the only one that
is is 2x LPlas/2x M Disruptor (and even then the two medium slots are functionally dead against armour).
And that's the energy preference AI, the only one that really mounts strong anti-armour at all (albeit it does love disruptors to an unreasonable degree, midgame it's not uncommon to see it mount nothing but because it weights researching them quite highly, again GG if you have armour because they have no AP). If it was Kinetic Preference it would be loading up on trash like autocannons.