I'm not a newcomer though, I've worked on both cheats and anti-cheats going back more than two decades. I know how the sausage is made and it's not pretty.
The anti-cheat companies you talk about mostly sell a mass produced product that works very similarly to anti-virus software. Games embed the anti-cheat module and its cheat definitions get updated. Statistical analysis requries both knowledge of the specific game and access to its database. Often also additional game programming to even store the crucial data. A bespoke solution. This can't be mass produced and is expensive, so most games don't have it.
So to bring it back to the newcomer question, I thought this would work, why doesn't it?, the answer is that game companies don't want to spend the money. [1] A classic answer to most annoyances in life, really.
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[1] An interesting outlier is the online gambling industry, especially online poker. They spend way more money than non-gambling game developers and have much more sophisticated anti-cheat systems, including statistical analysis. It's also fun to see how techniques used to get around online poker anti-cheat detection slowly make their way into mainstream gaming with a delay of about 15 years or so. As a simple example, nobody serious was even running their code on the same system as the game client back in 2005, instead parsing the video signal and simulating HID inputs. [2] Took more than a decade to see popular cheats for regular games go to that length to avoid detection. Not because the cheat developers were less capable, but because the anti-cheats didn't warrant the investment.
[2] Thus taking the battle almost completely to the statistical analysis realm. Are your mouse movements random enough, with good jitter? Does your bot take belivable micro breaks? Does your average performance, including reaction times, degrade at the end of a long session as you get more tired? Et cetera.