I don't have a good intuition about the what makes a problem sensitive to tuning, is it possible there are a large number of control problems where proper tuning doesn't matter much? Or the deleterious effects of improper tuning (like oscillations or overshoot) are masked somehow?

EDIT: I guess intuitively, big (lots of inertia) damped systems are probably pretty safe--you can do all kinds of crazy things with the control input and it won't really have much effect. The only way you could go wrong is drift.. Anything that is inherently stable seems like it should be "easy"--like a high-wing monoplane with lots of dihedral angle, you release all control inputs and it defaults to straight and level flight.

Yes, you’re absolutely right, systems that are default-stable are much easier to tune, and large inertia does make the system more stable. For those sorts of systems, any minimal feedback is often enough to get the performance you want. If you have high requirements you might need something fancier, but frankly most systems don’t have high performance requirements. Having very fast feedback loops helps too, so with digital controllers getting better and better you can be a bit sloppier with control design and it will still work.

There are indeed a large number of control problems where proper tuning doesn't matter much. I think we’ve built many of our tools to be “easy” to work with, and one aspect of this is that they’re intentionally made in a way that’s easy to control. Another factor here is that the “difficult” problems need some serious thought, which require research, measurement, and advanced degrees, making them more expensive. Many of these are just not worth the cost (yet). And even if you _do_ design a well-performing complex controller, you need to hire controls engineers to maintain and update it as designs change. I _love_ using LQR, optimal control, robust control, etc, but can almost never justify it. As a result, probably 90%+ of control applications by count just use PID. The remaining 10% are of course where most of the research happens, they’re much more fun.