They've done amazingly well on just Instagram with the groups they are targeting. I doubt that a website would have any impact on their business. In fact Instagram gives them something much easier, more visual, and with a built in social feed (no need to setup a mailing list, just use Instagram).
"But it's a walled garden..." - Most people don't really care. And also, it's a coffee shop. If Instagram shutdown, they'd be on the next platform in a week and rebuilding the same following.
It's annoying to people like me, but don't see it changing anytime soon, and I can't really blame the business.