Unchecked H&H, poor knowlede of the proper use of AI's and yoyoing hormone levels due to poor implementation can all lead to physical and or psychological issues that are in fact unhealthy.
Sure, we can come up with an extreme case that's bad. Just like drinking too much water, too fast is bad for you.
I've worked as a physician inside the VA Healthcare system. I am fully confident that most of those physicians responsible for that 80,000+ vets on TRT fell on the side of relatively incompetent in TRT implementation. Yet, even the people who were treated inappropriately did better than those who were not treated. A truly and symptomatic hypogonadal person, in my estimation, is likely better off physiologically and absolutely better off psychologically than someone who is untreated, even under less-than-ideal circumstances the majority of the time.
Now, if we go to the other extreme that BBers on these forums do where they're trying to get the largest possible dose that their physician is willing to prescribe, and that is likely outside of their bodies own physiologic norms even if technically near the upper limit of the reference range, then sure... excess T -> E conversion, drug-induced polycythemia, etc. can cause some detrimental effects. Would they be deleterious? I'm not sure I can answer that question. It's plausible to suggest, but I'm still not sure that's true.
Psychological issues in baseline psychologically normal males is not something I'd be concerned with. There is no shortage of studies already demonstrating that testosterone induced "roid rage" is a myth. But, when it comes to anxiety and depression BDI scores improve about 10 points on average after therapy is initiating--and they persist! That's often the difference between no depression and depression, or "I want to kill myself depression" and "I just feel down". Huuuuuuge differences.
The biggest thing people have to risk is starting TRT when it's not necessary. That's what people should be avoiding. And, physicians who play loose with peoples HPGA to keep patients happy are doing them a disservice and I'd argue violating their fundamental oaths.