I dare say it is true that some parents use screens instead of talking to their children, but I remember being expected to be quiet when adults were talking - over coffee, on the landline, anywhere. It's not as though we have gone from halcyon days when parents connected with children, listening to them and talking to them properly (as opposed to correcting them, getting impatient, telling them not to interrupt etc) to a state where children are routinely ignored in favour of phones.
Also, I suspect that underpinning this idea is research* into different codes of speech, which suggests that 'Elaborate code', as used by most middle class families is given higher status than 'Restricted code', which is used by both middle and working class families. Restricted code relies on gestures, partial sentences and shared contexts, so we all use it amongst friends and families, and Elaborate code is more objective and context-free (think voice-overs in documentaries, or political speeches), and it is used to discuss more complex ideas. As elaborate code is not always used in working class family life, children can struggle with it when it is used in school (eg in teaching), which can put them at a disadvantage compared to middle class children of similar intelligence and ability. Anything that closes that gap can only be a good thing, I think.
Also, at interviews for university places and many jobs, communication styles are very important just to be given a chance to show what you can do, so if debating skills and rhetorical strategies can be taught from a young age, again, the playing field can be levelled. Exam questions have to be written in Elaborate code, and text books are written in it, so the sooner children become as fluent as possible in Elaborate code the sooner they will be at ease with it, which will open many educational doors.
*Restricted and Elaborate codes are now dated terms (I'm not sure of the more modern and acceptable ones as it's decades since I studied this sort of thing), and further research into dialects and 'street talk' has shown that there are very complex patterns in so-called Restricted code, but the point here is that it is not given the same status as Elaborate code, so it is important that all children are taught to use both codes equally and appropriately in different contexts.