Is chanting a mental exercise?
Chanting Hare Krishna is supposed to give the mind a rest. The mind is constantly active, feeding us questionable information about what's attractive and important. The mantra frees us from all mentally concocted propaganda, such as the major delusion that our body and our self are the same. By chanting Hare Krishna with attention, we bypass the overactive mind entirely.
Here's a mental exercise: try chanting "Coca-cola, Coca-cola, Cola-cola, Coca-coca" for ten minutes straight, and notice the effect it has on your consciousness. "Coca-cola" is the registered trademark of a beverage company, and a name for a particular brand of sweetened, fizzy water. By chanting "Coca-cola" we do not experience the sweetness, fizziness, or thirst-quenching quality of actual Coca-cola. The beverage and its name are different. Only an unreasonable person would persist in such chanting. How could it be anything but unsatisfying?
On the other hand, the Hare Krishna mantra consists of names of the Supreme Person, the eternal and ultimate source of all existence, peace, and happiness. Believe it or not, chanting Krishna's names brings us directly in touch with the Supreme Person—in the form of sound. This can give us more peace and happiness than any amount of mental exercise or Coca-cola can. Those who have experienced the pleasure of chanting Hare Krishna would prefer to not do anything else.
The "mental exercise" involved in chanting Hare Krishna is the constant effort we must make to drag the mind back from other pursuits while we're trying with our lips, tongue, ears, and vocal chords to chant and hear the mantra. The mantra is Krishna Himself; it can give us all satisfaction, provided we pay attention. The workings of the mind can't give us any peace or happiness.