If it's ingredients that they use anyways then instead of using some back closet for storage they can simply put them out on display.

While tidy conceptually I don't think the economics and logistics work for that - retail space is more expensive than storage. Even if the ownership could be worked out to stock the same thing competively it would make more sense to get it from shared storage than use the more expensive retail space.

Said assumption also isn't trivial in terms of "what people want to buy vs what is sold".

There are some specific exceptions. For example, it's not that unusual for "artisan" sandwich places to also sell their bread. But it doesn't really make sense to imagine a pizza place that also had un-prepped mushrooms, green peppers, etc. out on display for separate sale. It's just not their business.

A finished "artisan" bread is high value-added product with great margins. Can you also imagine if they selled flour and tried to price it at a similar multiplier as the finished bread