Won't argue with the your observation on consumption: I see the same with my children.
However: there's nothing intrinsic to the BBC that requires linear delivery or consumption. iPlayer was, after all, one of the first streaming services: a genuine bit of innovation from the Beeb.
I dearly want to see the BBC not only survive, but to prosper.
That may be rose-tinted/delusional/whatever. Why? Because it represents a collective service for society, by society. I don't watch all the content: not even some of the big stuff (Strictly). But I really value the breadth of content: that it caters to interests - people - that are diverse. It can do that because it doesn't have to slavishly chase advertising in a race-to-the-bottom death march to mediocrity.
Similarly, its aspiration to impartial news coverage - to inform and educate, not impose a political doctrine - should be invaluable. It certainly hasn't always achieved that (and sometimes by a long way) but at least the aspiration is there. It would be greatly helped here by some structural protection from government meddling, but that's another story.
Like the original article, I see the writing on the wall. But I don't think it needs to be a death spiral. In a world of hyper-targeted-advertising-driven-sensationalist-fact-free-fake-news in 140 characters or less, I want to believe there's a market for diverse, challenging society-enhancing content. I can't think of an organisation whose charter would better fit with that aim.