Cortisol isn't inherently good or bad. It's context-specific. It's not something you want to universally lower. In fact, if you take supplements or medicine that significantly lowers cortisol (e.g. by inhibiting cortisol synthesis) you'll find that you don't feel very good at all. You need an appropriate amount of cortisol to respond to activities.
Running extreme amounts (100s of miles per week over and over again) should be approached with additional education and appropriate attention to one's health, but generally speaking someone running for fun and paying attention to their body (e.g. don't force yourself to run if your body is telling you to take a break) doesn't need to worry about anything.
That said, I've been a competitive distance runner for over 40 years. What adverse effects should I be seeing? 'cuz I can't think of any.
The article this idea comes from is based on the idea that long distance runners spending their whole runs at 80 - 85% of their max heart rate. That’s only about 20 seconds off my 5k race pace if I want to compete at that distance. There’s no way that I’d keep that pace at distance - my coach would fire me, I’d be an idiot and I’d overtrain myself into oblivion.
Mark Sisson’s entire idea is based off of the idea that long distance athletes train at what’s called tempo pace. Tempo pace is about 80-85% of maximum heart rate.
He went on to argue that consistently training at long distances increases cortisol levels and said this is bad.
There are two problems with this. First, distance runners don’t do all of their training at tempo pace because that’s stupid. Second, cortisol isn’t all bad - the body needs to be over stressed at points in order to create the adaptations that we are exercising for.
Point being, you’ve got to be careful just like you are with any form of exercise. If you destroy your body day after day for long enough, bad things will eventually happen to you.
The important thing to always remember is that more runners die from drinking too much water than die from not drinking enough. Everything can and will kill if taken to the very extreme.