I think a varied diet is excellent. Thinking paleolithically, it's extremely unlikely that societies - when not confined to say, an island- had to maximize the resources available to them. That is- they didn't go out everyday and get a leg-o-venison from the local herd- they'd also throw in smaller/other things, varying with the seasons. (Say, when they were getting to the end of a deer, they might make a deer-and-rabbit stew, if the deer lasted that long.)
That, and if a group of people was nomadic- which from what I understand is likely, even if it was "only" a seasonal thing (summer hunting grounds vs winter, for instance), different food would be available at each location- and even the "same" food- let's say apples- may have a slightly different nutrient balance due to location factors, like rainfall, soil type, etc.
However, I'd also take into account the issues of modern life before believing that you have to/should/whatever eat a varied diet, whatever that may mean. Perhaps you have a food allergy/intolerance (or lots of them), or even something as simple as there being no good spinach-grower near you, or you may even be recovering from an eating disorder. Take those sorts of personal environment factors into account, do what feels best and works for you, and rock on. It varies so much from person to person- I don't think I'd feel comfortable saying "yes, you can limit yourself to X, Y, and Z and that will BE AWESOME."
(and as an aside- I personally think that when transitioning to another way of eating for health reasons (not just weight loss) that an elimination diet, to whatever extent you're comfortable with, is the way to go, and gradually add in things as you sort out what works. Scientific method, n=1, etc etc.)