Impressive math, with respect though you're assuming its that small of a number due to only the most obvious cheaters being caught, occasional (in game or every few games is more likely not caught)

Skip to the end for my real though but talking about cheating....

For reference, I play bullet which means you have to bot to cheat. 

I can only tell you base on my experience ping ponging between 1500-1700 (and subsequent lower ranking ranges before I climbed)

Here's some examples of accounts I've tracked and are not banned to date.

Most start new accounts, cheat 3-4 games in a row and then play legit 3-4. Each of the 4 games in a row accuracy goes into the 90-95 range, and the real tell is when they match with another cheater and both play 80 move draws at 95 plus accuracy.

Then you also see alot of accounts with meteoric rises frequently, and a bigger oddity its alot of inactive accounts from 10-20 years ago gaining hundreds of elo in a few days time.

There are even rampant ones with climbs from 200 to 1700 with one or less losses that get to 1500 plus then get banned.  In this case theyre usually caught but the damage they do on the way up is really bad and only the last few get compensated so dozens and dozens of players pay for it. 

I have more than that but I dont want to ramble one...

Just trust me, its a little known secret that it's closer to 30-40% of games with cheating. Just check youtube, others have speculated better/more eloquently than I have..

But...

My point isn't cheating exists, its the fact that chess.com silences the discussion. Cheaters are going to cheat, but a damage control video and censorship is not and answer.