Charlie,
There’s a difference, in theory, between your first two examples and your third.
It is always, and unequivocally, an obligation to do mitzvos and not rely on Divine help at the expense of human effort.
For panassah and health and such, someone on a high enough level should rely on Divine help to the exclusion of human effort (as an example, Yosef with the sar hamashkim).
I doubt that there is anyone on that level in our generation.