The biggest factor in this 4 BC build is due to 3 factors:
1- the formula change to calculate Armor having the order changed (% is now counted before flat)
2- you only need 4 stacks of BC passive to account for the 30% reduction and a single player does have 6 slots
3- due to 1, any non-unique application of flat ArPen or ArRed will hurt a lot after % is calculated and BC has a non-unique ArPen

How to fix this:
1- Change the BC passive to: Dealing physical damage to an enemy champion reduces their armor by 5% for 5 seconds. This effect stacks up to 6 times. - This is to fix the fact that having multiple BC each applying a stack allowed a single player to apply the 4 stacks in one swoop. With that change it is no more possible except if the player wants to stack 6 BC. Maybe even lower the % to 4%
2- Change the BC ArPen to +10 ArPen or even +5 ArPen
3- Change the BC ArPen to be a unique passive and therefore stacking BC will not allow you to gain from that flat ArPen more than once

I think the biggest issue due to the formula change is the easy application of 30% ArRed (which on a 300 armor player means instant 90 AR reduction benefiting everyone). I would actually change BC with 1- and 2- (with +10 ArPen) in the above change proposal. Using 3- would be a too big nerf to BC.

ok so, true damage is a thing now, pretty much everyone can do it. Who cares? It's an easy counter, don't buy armor, buy HP. Same for all true dmg, buy HP is the solution. And I tell you with these new items you so can buy hp and dmg at the same time, there is nothing to fear.

It just doesnt even make sense that they'd make the Cleavers % pen stack, I assumed people were stacking for faster stack application and to get the bonus flat pen. The old black cleaver would only apply an extra stack per hit, still maxing out at 3, because it is a debuff. Why isnt it like that, considering the way that armor reduction doesnt scale multiplicatively. So now rather than just fix that, he's just gonna delete? I mean dowhat you gotta, but it doesnt seem that hard to fix.

What is the .88?

Looks like you're calculating as...

30% Reduction (BC full)
12% Redux/Pen
8% Redux/Pen
35% Pen (W)
Then the flat penetration of runes/masteries/BC

BC is pretty beastly, but alone it's roughly equivalent to LW (give or take). With Last Whisper it's a bit more dangerous (necessitating some HP, not a big deal).

Stacking BC probably isn't going to break a good team (they'll start getting health and have a frozen heart to reduce your DPS by 20%), but yah it's pretty powerful.

Though a full gimmick build is going to greatly reduce your potential DPS from alternative modifiers unless you're an AD caster. That HP tho 0.0

12% is from the Dominion global aura. This was covered like 5 posts before yours.

Unless they changed it. it is possible to have negative armor. so.. some of these calculations would result in you having negative armor and thus taking more than true damage. no one

So just to to quote this formula.