Our garden is full of blackberries.
I pop out & fill an old ice cream tub with them every day - then, if it's the weekend, I make crumble or upside down pudding, & if not, I bung 'em in the freezer.
We also have a tree which is groaning with apples & usually make cider - we have the apples, a mate's dad has the press, we split the cider 50/50 - 4 gallons each last year!
However, a) this only happens because we are lucky enough to be relatively comfortably off to start with, ie. we have a nice big back garden with brambles & an apple tree in it. Schlepping miles to pick blackberries covered in road muck & exhaust fumes? Less attractive.
b) I always feel a warm glow when I make a 'free pudding' but it's bollocks, isn't it? Flour & sugar are cheap, butter & eggs less so, & then there's fuel. It's really not going to work out cheaper than a cheap pudding/muffins from Asda.
c) my dc get little pots of blackberries or an apple in their packed lunch all through September. They are already muttering that they'll be glad when we can go back to shop bought satsumas - or even just an apple that isn't small, hard, a bit tasteless & a slightly odd shape.
It's lovely to have the fruit & I make all the use of it I can - but it's never going to be a significant contribution to filling hungry children. & that's with it literally on my doorstep, not foraging for it! Daft idea, OP.