My sense is that once critical users/subscribers move elsewhere, the decline will come rapidly.
By "dead", I don't mean PSTN won't exist at all. But its status will be like Usenet or IRC: a system which technically still functions, but is a wasteland of deserted spaces and/or spammers and scammers, while the hub of discussion and commerce is found elsewhere.
There's a tremendous foment of alternative systems, though it's not clear if any one of these will emerge ascendant. It's quite possible that you'll see splits among major usage bases, particularly in business/commerce and/or personal messaging. The usurpation of direct realtime voice comms by texting for many (though certainly not all) uses is also a part of this.
A key point to remember is that once a large network with network effects enters into a death spiral -- positive feedback loop of decreasing value and increasing costs -- the end comes surprisingly quickly. And in both news and conversations I'm having with any number of people and organisations, dissatisfaction with the existing phone system is rampant.
The fact that what most people consider as "phones" are actually relatively general purpose computing, information, and comms devices, on which any arbitrary protocol can be layered, may actually be the kiss of death for PSTN. You won't need to buy a new device, only install a new app (or use the one that's been pushed to your device by the vendor).
For home and office users, the final merger of comms to the desktop (or laptop) system is likely to occur. Some mechanism for patching existing infrastructure to the new system(s) may work for older / hard-wired legacy installations.
What the replacement system offers, its specific capabilities, and how directories are handled, remain interesting questions. There should be both past examples of similar transitions (telegraph and TELEX to voice and computer messaging, particularly) which offer clues. We're probably staring at most of the pieces if not the complete system presently.
When you can't rely on the fact of any arbitrary business, organisation, and/or person having PSTN service through which they can reach you or you them, the end will be well in sight.