What's to stop someone who carries a phone from turning it off before entering the cafe? You can read those texts later.
If my home security system tells me that it heard broken glass, I want to know now, not in thirty minutes. If my kid needs to be picked up from school, I want to know now. If my spouse's employer calls to tell me they've been sent to the hospital, I want to know now. Anyone with a job that requires them to be reachable for emergencies (like an emergency responder on their lunch break) cannot attend this cafe. In today's society, it's a luxury to have no responsibilities to anyone such that you aren't reachable for hours at a time.
It's wild to think of a place that would be exclusionary of parents, caregivers, partners, and more simply because of an absolutist policy. And you've got to be carrying cash. And of course, there's no ATM because that would have a screen. For a huge swath of the population, this is simply a non-starter.
There are also those of us who can be on long flights, travel places without cell service, may turn off phone if international, etc. I'm mostly reachable by cell phone but, no, you're not guaranteed to reach me right now every moment of every day.
Luxury? For a large swath of the population, that’s called “a job”. From nurses to factory workers, many aren’t allowed to carry a phone when they go to work.
But, man, this idea that the leash can’t be cut for even thirty minutes to enjoy a coffee is indicative of other problems, IMO. Just because one can constantly be reachable doesn’t mean one should. Which is…kinda the point of the café, eh?
Reachability != carrying a phone.
For those working at a job that prohibits phones, they are still reachable, just that emergency contacts will call the workplace instead (where someone would then deliver the important notification in-person to the employee).