I've been ruminating on this for a while and have some observations.
Endurance athletes often run into situations where they have elevated cortisol and suppressed testosterone. I've read one pubmed paper about endurance athletes that concludes their growth hormone levels are the same whether they are in their competitive season or not. This may or may not be meaningful as it didn't really evaluate their growth hormone levels as a function of training loads and often the 'off-season' means a lot of long aerobic training sessions.
Also, let's acknowledge that high cortisol levels has it's place. The problems arise when we get chronically elevated levels that never drop, which runs into adrenal fatigue. As a 'stress hormone' cortisol triggers inflammation, which is a healing mechanism. It also provides pain suppression, which is an interesting effect. From a sports perspective it's seen as a negative because it is catabolic, but this is just a side effect of it mobilizing protein into glucose. It's a way your body is providing energy for activity. Of course mobilizing this glucose also raises insulin levels encourages fat storage in the belly, another way for your body to provide itself with long term energy. Like every other hormone, it's neither 'good' or 'bad', but a necessary part of the cascade your body uses to keep itself balanced. We see it as a negative because modern society is so screwed up it works against us.
If anything in this whole equation is 'bad', I'd say chronically elevated stress is the culprit. Your body has evolved to deal with a short fight or flight scenarios followed by a moderate amount of low-level activity around a camp and plenty of sun/sex/sleep. Our society has very few true 'fight or flight' scenarios but long periods of elevated emotional stress. We tend to push ourselves really hard at work sitting at a desk, driving, etc., then put ourselves through really tough workouts (Crossfit, Ironmans, Adventure runs, etc.) and take pride in our lack of sleep. All of these things are asking for adrenal issues. We never give our bodies time to recover and reset. It's no wonder we run into problems. Hell, it's amazing any of us avoid them.