Gatherer, hunting, and fishing gives you like 6 different foodstuff types. Fish, venison, and the four types that gatherers give.
My towns basically live off fish, though. 28 people spread out over 7 different docks.
I think the people need more than just variety, but I could be wrong. The town I mentioned above has fish, venison, mushroom, onions, berries, and roots along with their walnuts, pumpkins, and potatoes, but their average health had fallen to three hearts anyway. The performance of the workers was so bad that fields weren't getting planted fully and no wood was being brought over the bridge from the forester. The herbs remedied that but the average health is still only 4.5 hearts. I had another town that had corn, squash, and apples as its crops and it was perfectly healthy without an herbalist. I think this town needs something more, even yet.
On the other hand I did try the same seed on Easy mode and got sheep, cherries, peaches, beans, and cabbage so not all is lost. Easy mode is actually harder in some ways than Medium mode. In Medium mode I was starting with 10 adults and 10 children. In Easy mode I got 12 adults and 17 children. That was almost half again as many mouths to feed immediately, of whom almost two-thirds did not contribute to the effort. Plus, I hated the original layout on Easy mode so I immediately demolished the empty houses and rebuilt them elsewhere. The delay in planting was fatal. After two children starved to death I restarted. After two years of messy living I finally have the fields and houses where I want them, and only one breeding couple escaped their parental control in the process.