I don't think the goal is to get them to compete with casters, exactly, but rather to allow them to excel in their own spheres. A cleric who wakes up one morning and decides he wants to be a fighter can do so, and can actually do so better than the fighter himself can with equivalent resources. A wizard has a much harder time literally doing the same thing, but they have a bunch of extra resources to make it so that smacking somebody with a metal stick isn't as relevant.
A level 20 fighter should be better at fighting than a level 20 cleric, and the actual things that fighters do (eat enemy attacks, do damage with weapons) should be meaningful at high levels on their own merits. I don't necessarily care that a wizard can burn through an army of enemy grunts faster than the fighter, or knock down a building, or something equally grandiose, i just want the fighter to be good at what he is trying to do.