I agree with the advantages you talk about. However, sometimes I find that student totally understand the physics/math behind the brute force (though maybe the logistics is tough), when they can’t seem to grasp the analytical approach. This seems especially true when there’s some fancy math trick. The Brachistochrone problem comes to mind. In that, to do it analytically, you have to do a cute variable substitution. My students often say “they wouldn’t have thought of that.”