Indeed, the grandparent post is a pretty good summary of the takeaways you get from taking PADI’s enriched air nitrox course (which is a requirement if you ever want to dive with enriched air).
In the olden days this was tracked manually (the ratio of your depth to percentage of air and time under water) via so called “dive tables”. The purpose and output of the dive table is to determine the safe amount of time you could dive at a certain depth without risking narcosis.
As this is a sliding window based on multiple variables - and you are very rarely maintaining a constant depth as you dive - it’s of course annoying and less accurate to hand calculate this. Modern dive computers just seamlessly calculate it all for you nowadays.
Fun fact: those dive tables were created by the US Navy conducting experiments on its own divers, there was a real human cost to acquire that information.
Numerous other training agencies also teach how to use nitrox safely. PADI training isn't specifically required (or even particularly good).
I don't see where the person you replied to claimed there was anything special about PADI.