I don’t think the point here is the atual ban. R’ Shorr is stating what his opinion is regarding the frum community at large and surely holds that other shuls/ batei medrash should implement this ban as well. This is his shita as Daas Torah.
I agree that the practicle institution was only made for his kehila however, it is clear from the article the rav’s feelings towards texting in general- even out of the beis medrash.