I don't get bored on a limited selection of food, or at least on the set of foods I currently eat. I have a suspicion that what people usually identify as boredom really isn't boredom. At least that was true for me. I get a kind of restlessness sometimes where I will want something I can't have, like salted nuts or peanut butter or worse.
I know I have plenty of foods I like, but they're not the foods I'm presently craving. If you asked me previously to identify what the source of my discontent is, I'd say "I'm bored with these foods". But on further reflection, I know that isn't right. I love the foods I have available to eat and at meal times I eat them happily. But I'm hungry and hunger is good sauce. Everything tastes wonderful, I'm fully satisfied and contented after a meal and food is far from my mind. Absolutely no boredom with mealtimes.
But come the snacking hour (between bed time and dinner time) that restlessness sends me scurrying to the pantry looking for forbidden eats. That is not boredom... it is cravings.
I think really people normally eat very limited diets. But they're not aware of the limitations so they don't pay them any mind. However when they go on a diet, they're suddenly quite aware of their new limitations and mentally that makes them uncomfortable and they look for escape clauses.
I've given up foods for 2 reasons. One is that some make me ill like gluten, chocolate, nuts, seeds (*cry*) and dairy. The other list is ones that make me fat. The fat ones seem to set off binges so bringing them back "in moderation" just isn't going to happen.