While I mostly agree with your statement there's evidence that testosterone is linked to social status and mental well being.
A 50% drop most likely has a multifactorial explanation, being told that some traditional male traits are bad (and thus lower well being or social status) or medicated away (see e.g the rise in ADHD and Autism diagnosis) might have some effect.
I'm not nearly knowledgable enough to give any reasonable estimate but it would not surprise me if it was higher than 0%.
> testosterone is linked to social status and mental well being
As well as a zillion other things. And "linked" in which direction?
> might have some effect
Snow might have some effect on the height a mountain, but most people believe geological activity is more important than weather.
The relevant question isn’t whether something or another might have “some effect” it is how to reduce the main factors which we already know damage men’s sexual health. And spending time on the long tail of factors which may or may not be relevant is sucking all of the oxygen out of the room for addressing the factors we already know are most of the problem.