Does becoming good at scientific research force one to become one dimensional?
You can do it, but you might not be a professor. I have a PhD in Aerospace Engineering, and I work in CFD, HPC clusters, and BigData/analytics when I do research. My primary job is running the HPC department at a large-ish computing center. If I were a professor, I doubt I could pull this off. My research output is much smaller that professors my age, but I still have a pretty satisfying career. 

You best chance for doing lots of different kinds of research is to find a center who appreciates you for your broad interests and to help it grow its mission while pursuing your more esoteric interests when you can.