I might as well update here... I'm now a wild spinach convert, it is sooooo good thrown into cooked foods. I made feta-wild spinach crepes last week that I was just obsessed with, but I didn't trim the stalks at all, just the leaves.
I bought some recently and mixed a small amount into a salad that contained other kinds of lettuces. That is, I used it as an accent to a dish rather than as the sole green. You could certainly cook it if you wanted to, though.