Hunter-gatherers ate from hundreds of different food sources. The average western-culturally-deprived citizen eats, what, less than 50. They also fattened up in the summer, and semi-starved in the winter (at least, in the colder northern climates).
Absolutely, Bryant and Gordon. My family had home-grown frozen vegetables and home-canned fruit most of the winter but my husband grew up eating "fresh" produce all year round so that's a bit of a problem. I plan to grow plenty of good "keepers" like root vegetables and squash when we can tend the garden regularly (we don't live on-site yet) and hopefully we'll compromise
As for varied diet, my dad grew up on deer they could hunt all year, potatoes, cabbage and a couple hundred jars of saskatoons (serviceberries) his mom put up every summer. (That was a family outing for them: G'pa, G'ma and nine kids out berry picking.) My mom was even more limited: fat-beef broth on Sundays and milk sauce (flade) all week. They were too poor to even start a garden (!) and she said that in spring, the siblings foraged greens and ate them in the field like the goats. But they turned out to be the smartest, most resourceful people I know.
We all have to do what we can and make our way without the can'ts.