Another AP/Armor option would literally break AP champions.

You'd have mages/AP bruisers building both Zhonyas and 2nd AP/armor and be incredibly difficult to kill for all non AD carries - and even then, AD carries would have a slightly more difficult time to kill them and that slight time increase could be the difference in an AP being able to use another rotation of spells just because they can absorb more damage.

I don't know about you, but that sounds hilariously broken to me. APs already get tons of double dipping in HP/MR in their items, which also provides a nice chunk of AP and typically a strong passive/active and CDR along the way.

ADs don't have a pure AD/armor option either. Sure, you have but its damage falls off like a rock and doesn't give AD. You know why they don't have AD/armor items? Because it'd break the shit out of bruisers too.

in short, making an armor item that provides straight offensive stats would be broken. Zhonyas is an exception because it gives mages some wiggle room dealing with assassins/bruisers/adcs between cooldowns and the active is the best active in the game. If you added more, you would seriously break the game.