From someone who might be pursuing a physics degree soon.
> Some of us learn in graduate school that we can't spend our whole lives solving one problem.
Would you please expand on this. I am not sure if you meant that problems are hard enough or what.
The nature of a PhD is to study one sub-discipline long enough to reach the edge of human knowledge, and then expand it. Often this is so difficult that a set of multiple diverse projects is not practical. But not always; in my PhD I worked on both astrobiology and solar cells. It helps to learn versatile methods that apply to a range of problems.