I think the issue is that it's basically telling people who require their phone for things like medical devices that they're not welcome in the pub.
That is potentially a very big issue for the pub chain in terms of the disability discrimination laws, as for example there are hearing aids that use the phone to make adjustments, partially sighted users may be using the phone as a "reading aid" for the menu (it's either acting as a magnifier or reading out the text), diabetics using apps to monitor their blood sugar (IIRC there are glucose readers that connect to an app to log your readings automatically and give advice) and those are just the obvious instances, whilst people with allergies may be using the phone to check what's in something.
I can understand a "no phones" policy if it's enforced within reason, but blindly banning them regardless is going to lead to issues, as increasingly a lot of things that used to be done via separate specialist devices are now being done either through the phone or with the phone as the controller because it makes them easier/more user friendly (this is especially true of medical devices and disability aid - I remember when things like reading aids for the blind were massive, expensive and not portable, now a half decent phone with the right app can do it anywhere).
All it will take for the pub to potentially face a big fine is for one person who uses their phone for something medical/disability related to make a complaint or take legal action and it's potentially a very straight forward case (as the law only requires "reasonable steps to accommodate" from the business, and in this instance there is nothing unreasonable about allowing things like the phone as a disability aid as it costs the company nothing).