It might sound a bit daft and a drop in the ocean, but what's not to like about the idea? It won't do any harm and, although it might not do much for children's communication skills it might just emphasise, for any trainees who may become parents in the future, the importance of talking to your child.
I think we'd do well to remember that the parents of today are our children of yesterday. So before we start condemning them it might be as well to reflect that it could be the culture, which we created, which they experienced while growing up that has produced the parents we're so disapproving of.
As for our position on international tables for reading, that's a whole different can of worms which I've been involved in for a long time and won't go into here. But it is important to point out that we get a huge amount of our vocabulary from the written word (proven by research which I can find if you wish to contest this) and that, as the ability to communicate well is highly dependent on one's vocabulary, if children aren't reading (either because they can't read or because of screen time) then they aren't extending their vocabularies.