Agreed. Another OneNote user here. Wife is on Android and her OneNote is synched to our shopping list on OneDrive. Works beautifully.
Yes it really does. Been trying all sorts of apps from the store, but they all proved waaaay to elaborate.
Somehow I found myself reverting back to pen and paper every time.
Since I tried Onenote I never picked up a pen again. Whether I'm @work, @home on laptop/pc or even TV, I can always view and update any shop list, similar to you and your wife's approach. Always available and always up-to-date.
I personally found Onenote to be the first app ever to actually be more efficient for shoplists than writing on paper.
Little off-topic, but why stop there ? That app is virtually limitless for a thousand purposes. You can create entire archives of all kinds of information in the exact same efficient manner, and it is always up-to-date and at your fingertips on any device.
Lately I'm planning everything through that app. Calendar actually comes second in my household ;-)