Udyr, Xin Zhao, and I think LeBlanc were all hotfixed due to balance issues. Cleavers are game-breaking. Both teams can buy them, but both teams could pick Xin/Udyr/LeBlanc in normals, and could be banned in ranked (although I don't think ranked was out for udyr/xin).

the xin zhao nerf hotfix, leblanc nerf hotfix and riven buff hotfix disagree with you

1. Look at the word "Usually".
2. How long ago were those things? Riven was released in September 2011.
3. The most recent "Hotfixes" for balance have been mostly a day or two after a champion came out or more likely they were essentially mini-patches before a big tournament. This is the pre-season, so you don't get to expect everything to be balanced - they even said it'd be shaky in terms of balance when they introduced it.

How did you come up with this set of changes to fix the issue?

1) I don't see this as a problem. Brutalizer has always stacked with others.
2) Bringing this to ~25 is probably a reasonable change so long as the math makes sense.
3) Pretty big nerf. Would Black Cleaver's flat pen still stack with itself? What about the item cost?

I realize its a forum, and not great for mathcraft, but are the numbers making sense with all the changes you mentioned factored in (including the removal of the global pen)? Surely you have the item data and champ stats to put it in perspective.

A major objective of this patch was to make AD casters more viable. I fear that the pendulum is about to swing the other direction in a big way.

Judging by the comments, the player base wants the flat pen on BC to be unique. Why isn't this a good solution? Can't we just make a White Cleaver with the stats we want?

This is a bit of an abstract, but I think that the cleavergeddon is a few things all happening at the same time.

1 - The order of % and flat pen was swapped, making flat pen more powerful.

2 - BC provides an additional 30% reduction which didn't exist before, allowing % pen to reach 70%+ for many champions, even before accounting for flat pen.

3 - BC itself is an outstanding item for any AD champion. There are no wasted stats for anyone and it's extremely efficient.

4 - Many of the champions with large % armour reduction skills are the ones who benefit the most from BC itself, and were already strong champs on Dominion.

Any one of those things isn't in itself a bad thing, but all combined together it's too much, too sudden.

The BC nerf targets #2 by a small amount, and #3 by a fair amount (or a very large amount for each BC beyond the first). It should be enough to end cleavergeddon, but targeting #2 by removing the % reduction entirely from BC would be my preferred option.

The real issue you missed is that aside from #1, they also made resistances quite a bit more expensive, and the end-game armour items usually give less armour at that.

nerfing/removing BC won't fix a thing.

Riven released: September 14th 2011
Riven hotfix balanced: September 20th 2011

No need to nerf Brutalizer... You're changing the wrong thing

That was a year ago, dude - "Oh no you can't say you don't do X, during beta you have!" >.>
Also, as I noted, they're more likely to hotfix a champion the week within their release, that's the exception more than the rule.