OP is correct on every point but downvote train cannot be stopped.

People forget that beyond armor penetration, Black Cleaver also gives 15 more AD and 30% AS. Also, armor reduction affects your entire team, while armor penetration only affects you.

IMO, BC is generally better, but it's also much more expensive.

Midgame and early black cleaver will do more damage and help your whole team do damage. Later on pending how much arpen you have you may want to sell for last whisper, as the sale cost of blackcleaver alone will get you it. However if you have a lot of armor pen in your runes/masteries and perhaps some build into your champion, and if your opponents are not above say 150-180 building a ghostblade along side the cleaver will give you a huge dps boost.

Its just a case of reduction vs penetration. If I can reduce a squishy's armor to 10 with 3 stacks of BC, thats more than 40% penetration. You also get more attack damage, and attack speed on top of that. The 200 armor math involves the attack speed and extra attack damage, although probably not the extra 700 gold. Black cleaver is more efficent at killing squishy targets, and it does it for your entire team. In just the armor passives, It breaks even at 112.5 armor, and then you can factor the attack speed and damage.

To me if you're ad carrys kit revolves around auto attacks you should get a BC asap. If you rely more on burst from skills you should get LW. Like BC on Ezreal would be a terrrrrible idea, but on Vayne or Twitch...its an option.

Also upvoting, because while i may not agree completely with the op or his slightly patronizing attitude i think that this is a good topic for discussion.