So are "natural" and "grow-your-own" incompatible?

No of course not. You just have to grow enough for all of you!
I have tayberries. The birds have the top ones, the rabbits have the bottom
ones and I get the middle ones. Admittedly I also allow a considered
quantity of bindweed which hides some of the fruit and provides a convenient
handle with which to move the branches around.

E