The BPHs are quite happy to hemorrhage market share so long as they meet their HQ quarterly financial targets.
Most of their "problems" stem from their mandated priorities, where reporting ever-increasing gross revenue trumps unit sales, and where controlling print channels trumps reader or author interests. I don't see them disappearing, either, because they have a treasure trove of copyrights they control and can exploit for the next century. The scenario I see developing is they keep on buying other tradpubs and/merge together so they can keep reporting quarterly "increases" while laying off more and more production staff. That can keep them going for at least another ten years.
In the meantime they will continue to acquire IP from legacy authors and newcomers still willing to submit. They will be seeing less manuscripts but with less bidders (because of the mergers) they won't see a shortage any time soon. Over time, they will be reducing their output and focusing on proven big sellers and they will start producing more in-house content via work-for-hire contracts and in-house staff. (They are already talking about that.)
As their big name tent-pole authors age and "retire", I expect they'll start doing Tom Clancy type contracts, buying out their names and IP so they can keep on producing ghost content under their brands. Think of Patterson's book mill, only run by Penguin or Hachette. Since good writers come up with story ideas by the dozen, far more than they can ever write up themselves, they can buy enough plots and story summaries to keep their IPs running for another generation or two.
Basically, the BPHs can maintain their internal practices indefinitely, just by ditching their riskiest buys and adopting the book mill model of the pulp days. Which means they are under no immediate pressure to change their pricing strategies. In fact, they might be happy to see their new title ebook sales very slowly erode to near zero if they can still meet their quarterly financials along the way. In their ideal world ebooks would be solely for backlist: that was their very first strategy, after all, windowing ebook releases. I suspect they'll return to it, doubling down on a print first model after their Agency Part Deux contracts expire.
They still have plenty of options that don't require lowering prices any time soon.