All this talk about armor screwing BotRK up is honestly pretty useless. Irelia never did a lot of damage to tanks, and this didn't change a lot in S3. BotRK fixes 2 big issues S3 brings to Irelia, carries getting warmogs and people rushing warmogs as first/second major item.
Currently, rushing warmogs really screws Irelia over, especially if you are against champions that don't need a lot of offensive items, like elise or garen. BotRK fixes this issue, since it's very hard for champions to get large amounts of health and armor at the same time early game, and if they do, chances are they can get offensive items and screw you over harder.
Carries late game really won't be getting a hell lot of armor, and if they rush warmogs BotRK should add a good 50+ dps or more to your damage (remember, BotRK gives AS), along with a bit more survivability and a great passive for a medium amount of gold.
So personally, I'd probably rush it if my laning opponent rushes warmogs, or get it as my 3rd/4th item otherwise. Wit's end/zephyr are great alternatives if the enemy is not stacking a lot of health, but I don't think it will be happening all that often.