There have been several attempts at doing the same thing in the U.S., but none of them ever worked out for various reasons. Often it was because of the expense of upgrading the tens of thousands of TV transmitters across the country.
This one died in 2011: https://en.wikipedia.org/wiki/MediaFLO
In a small country with more centralized control of broadcasting and less territory to cover like Japan and Korea, it's much easier.
https://en.wikipedia.org/wiki/Digital_multimedia_broadcastin...
https://www.bbc.co.uk/news/entertainment-arts-44722812
Actors have vented their fury at two audience members who watched England's World Cup penalty shoot-out on their phones in the front row of a musical.
Titanic The Musical actor Niall Sheehy said the women "not only followed the penalty shootout on their phone, but also said 'yesss' on each goal scored".
He declared: "You are the most ignorant audience members I have ever had the misfortune to perform in front of."
Rude people are always going to be rude, and we shouldn't worry about the technology that enables them to do so. If they couldn't watch soccer during a musical, they'd just be coughing loudly or rummaging around in their pockets looking for a mint or having a too-loud "private" conversation with the person next to them.
Phones have changed nothing.
Seems to me that theatres (and cinemas) should be putting passive farady cages to block signals coming in, I'd pay extra for that.
They got paid to perform a play. There is no more obligation for the audience members to pay attention than there is for someone to eat all the food on their plate at a restaurant, or use a device they bought every day. If the women weren't disrupting the other audience members then the actors shouldn't have cared (and if they were, that's a problem for the house staff to sort, not them).
If actors understood that it's not the audience who is privileged to watch them act, it's them who are privileged to be paid to play make-believe on stage, the world would be a much better place.