Should global reductions `compile` internally?

Global reductions such as `nodal_min` must compute and evaluate the local reduction before passing the result to MPI. The code for these local reductions is not compiled, so It seems like they would incur the cost of generating the kernel each time the reduction is called? Should they perhaps have a memoized `compile` on the inside similar to `compiled_lsrk45_step` instead?

(Not sure if this has any real performance impact, I just noticed it while discussing with @MTCam and thought it was worth mentioning.)