I was wondering whether it is necessary to reinstall the CUDA toolkit after a drivers update.
I think that the tools are compiled with nvcc, which is installed with the toolkit, so I think it should not be necessary, and one can simply keep updating the drivers as soon as a new release comes out. Correct?
Correct, you can keep updating the drivers while keeping the CUDA toolkit “as is”. I am still on CUDA 7.5 but update my driver package every three months or so.
Note that new drivers may introduce new problems. For example, a driver update some months ago interfered with Folding@Home (which I run); as far as I know that specific issue has not been resolved yet: https://folding.stanford.edu/home/core-21-openmm-gpu-issues-with-new-windows-nvidia-drivers-375-57-and-375-63/