And I learned a thing or two about stress when I studied psychology.
Here are my thoughts (without sources and a bit worse editing as I am on my phone).
> I certainly crave challenging problems.
When crave something I always wonder how it is different vs a cocaine addict craving cocaine. I crave mental stimulation as well, so here are my observations:
1. Psychological addiction is possible.
2. Craving too much mental stimulation could weaken your social ties depending on how you seek it out.
3. You become intellectually sharper at whatever it is you’re stimulated by but in almost all cases not sharper in other areas, even when skills are transferable (unless the areas are really close).
4. As almost always, following a chronic crave does not make you happier. Like scratching an itch doesn’t make you happier.
Being frustrated is not an issue in my opinion. Frustration results from not achieving your goal while you believe you should still be able to progress but somehow you don’t. There is no stress there as you can simply do something else. Take the option of doing something else away and then you do have stress (e.g. this wasn’t a frustrating hobby problem in your free time but a problem on your job that is making your company lose $10k per hour).
> I worry if the type of person who seeks out stimulating work and having that become a source of stress is risking damaging their health in the longer term
Only if it is chronic. Read about the HPA axis. It proposes a biological explanation for depression through stress. Also, burnout is symptomatically very similar to depression (I am on mobile cannot find the source now, but any decent search engine can help).
> I always vaguely assumed thinking hard about problems was a net positive for my brain & would keep me mentally active
In this particular case the exercise analogy works. If you do anything physical (or mental) that is beyond your capacity or stamina but you somehow are forced to go through with it, then you will experience stress.
In closing only chronic stress is a bad thing since we can recuperate from temporary stress. Aka we simply need the ability to rest and the ability to recover.
On a short-term basis, stress is a good motivator to some.
Related to all of this (in an unusual way) is the self-determination theory of motivation. What you may see here is that in my examples people have little to no autonomy and that results in stress.