Medicine can help, but they're not a silver bullet.
So it could just be that the people you've noticed are just people who are more likely to develop these problems.
And if you want an anecdatum, I have ADHD, unmedicated during most of my childhood, and I went to develop all of the above except for psychosis.
Moreover, delayed diagnosis ADHD is even _more_ correlated with issues like anxiety than the ADHD population in general. If you think about it, that outcome is predicable: a lifetime of experiencing the kinds of problems created by executive dysfunction (especially with little or no understanding or explanation of the phenomenon) is a perfect breeding ground for anxiety or depression or both.
I'm not sure if the same statement is true for diagnosed but untreated ADHD, but certainly seems plausible.
Absolutely, you are correct. To be clear, that's 100% a hunch I just posted, based on no data or experience other than the people I have known that long who are now adults. Funny thing, a lot of them are deciding not to medicate their children.