I wouldn't go as far as damage, because it is reversible. If you stay away from saturated stimuli you relearn to taste subtler nuances.

Capsaicin, and similar substances (TRPV1 agonists) which are found in hot peppers and ginger do kill nociceptive neurons, but that's AFAIK the only case where some food directly damages your nervous system.

I think food addiction is mostly reversible (it may be easier to relapse than to become addicted in the first place).