If people wanted to have a website, they would. The truth of it all is that most people like the walled garden, the sandbox, etc. It's predictable, it's knowable with limited effort, and it creates the desired illusion for a nominal fee. There is no revolution to be had, the people have made (and are continuing to make) their choice. This is technology at scale, for better or worse.
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.