Why not black cleaver on ashe?

I'm only a gold 3 scrub, but ashe and jhin are my two favorite adc's. My last game I went black cleaver on ashe instead of last whisperer and it seemed to work extremely well.

Since her q pretty much instantly stacks black cleaver, and black cleaver reduces TOTAL armor not just bonus armor like last whisper, wouldn't cleaver be the better option against teams without multiple tanks? Average base armor at lvl 18 is around 80, so lw doesnt remove more armor than black cleaver until the person has 160 bonus armor, which is 2-3 armor items.

80 base armor + 160 bonus = 240 total Black cleaver reduces that by 72 ( 240*.3 = 72 armor removed) Last whisperer ignores 72 (160*.45 = 72 armor ignored)

BUT if they dont have 160 bonus armor, lets say they have one armor item for +50

80 base + 50 bonus = 130 total Black cleaver reduces that by 39 (130*.3 = 39) Last whisperer ignores 22.5 (50*.45 - 22.5)

So against a target with less bonus armor, cleaver reduces more armor, and unlike lw that reduction works for the entire team.

The only reason I would imagine lw being better on ashe than black cleaver is if A. Youre against a team with 3 tanks B. You really need grevious wounds But in the situation where youre fighting people who have at most 1 armor item, black cleaver outdamages lw and gives more survivability with the HP and movement speed and everyone benefits from the reduced armor. So why not go cleaver instead of lw on her?