You won't find enough berries, never mind edibles berries if everyone in your area suddenly shifted to foraging. Game animals would be exhausted quickly or they would migrate further out from human settlements. Even if you had the skills hunting or foraging isn't all that useful anywhere around a city, especially if everyone else is doing it.
True, fruit and nut-based food forests, like those in the Pacific Northwest [1], seem to provide a significant, sustainable food source. Berries make a nice dessert + vitamins a few times a year.
Historically here in Maine, the core diet seems to have been seafood, freshwater fish, maize, Capreolinae, game birds, eggs, honey, roots, and greens. While only a tiny fraction of fish/seafood remain, deer are over-populated and make a fine sustainable food source, the limitation mostly being the contemporary appetite for venison.
The edible himalayan blackberry infestation that plagues all of the coastal PNW is widely available. It's almost impossible to kill and it fruits for long periods of time.