The Black Cleaver - A support item?

Spoilers: No, it isn't, though it might as well be, since it seems to have that same degree of stigma as any support-related item.

In this AD assassin-heavy meta, the worst thing you can encounter is a smart tank vs. four or five assassins, and no Ignites. Now imagine if there are one or two more tank or off-tank enemy champions, and they all are smart enough to build a Thornmail or Omen; hell, even both! Most players' immediate response is to build a Last Whisper, but let's think about this for a moment.

The Last Whisper has 40 Attack damage and ignores 35% of the enemy's armor.

The Black Cleaver has 50 Attack damage, 200 HP, 10% CDR, 10 Armor Penetration and applies a debuff when dealing physical damage that damages the enemy's armor by 5% up to a maximum of 25%.

Depending on how many AD champions are on your team, getting a Black Cleaver might be a wiser decision. The Last Whisper ignores armor; it doesn't strip their armor away as a debuff. The Black Cleaver benefits the rest of your team. If you deal damage through sheer volume (Tristana, Vayne, Vi, Garen, Corki, Wukong, Pantheon, Jax, Trundle, etc.), a Black Cleaver opens up the enemy to additional damage from your team, and its effect is more far reaching than the Last Whisper. If you deal damage through nuking power (Kha'Zix, Nocturne, Rengar, Tryndamere, Yasuo, Draven) and you aren't a mage, then the Last Whisper is possibly more viable. Granted, there is no true AD nuke outside of Darius' ult, and even the listed AD nukers will also benefit their team more from the Black Cleaver, especially if most of the team is composed of AD champions.

So why doesn't anyone build it?