Such a place may not be for everyone and to me that seems fine. Camping is also not for everyone and that is also fine.
A cash only stance makes sense because paying for things will happen all day, every day. If your goal is no screens and that goal is in your name, that’s an impactful step to take.
If someone has a hypothetical medical device with a screen (do you have one in mind?) I’m sure the owners of such an establishment would seek to find ways to accommodate. It’s an edge case and not likely to impact the overall atmosphere.
But to your point, this is hypothetical. I’d rather that such a place exists and then learns how to deal with edge cases than not exist at all.