My experience is a little different: if I buy enough in game shizzle (be it free to play or games like WoW with a buildin store), I get away with murder.
> For a rough example of how the math works[...]
IMHO You are right about the math, but use the wrong parameters. Many game companies that accept additional currency actually allow their moneymakers to "bend the rules". No hard data, just my individual observations while using "tools" in different settings.
Your whole argument is also based on the idea that there is no such thing as bad publicity. This is incorrect. If your game gets a reputation for being full of cheaters then people will leave your game and probably not come back. If the first time you hear about a game, all you hear is that it is full of cheaters are you going to head out to the store to buy a copy?
Being so good at anti-cheat that there is nothing to talk about seems like something so far away it's not worth thinking about.
But that said, I doubt the gains from allow "controversy" around cheating would outweigh the benefit of not having any cheating in the game. Not having cheaters is it's own talking point. Withing the competitive gaming community, cheating is already a major talking point and having little to no cheating is already a major selling feature.
For a rough example of how the math works, let's say we have a game that is 5v5. If we have 100 players, 1 player cheating, and everyone plays once you end up with 9 players having their game ruined. That's 9% of players impacted by having 1% of the players cheating.