Rumors of DC's death are probably exaggerated. Perhaps there is some sort of stagnation though, or even some decline.
There are two sides to that:
1.) From the scientific side, only problems of which the solution can be partitioned into a tremendous number of tiny parts without (or only very little) interdependence are suitable for DC — this always was and will remain true.
While you could move such problems from DC to supercomputers right away, that would be a waste of the extraordinary interconnect power of supercomputers. And since there practically are no supercomputers with idle time, such moves won't happen.
The more realistic alternative to classic volunteers based DC would be DC in the cloud. It certainly is true that cloud computing has become much more accessible and affordable over time. But still, the costs are not at all negligible. Most scientific projects have to fight a lot for getting a budget, and if they luck out and get one, they have to spend it wisely.
It is true that available computing capacity in volunteer based DC cannot be controlled by the project owners. However,
– hobbyist projects basically have all the time in the world,
– a few platforms exist which have been hosting many different sub-projects for a long time now (longer lasting projects or/ and shorter lasting ones) and therefore have a good grasp on their available computing capacity, and thus on the planning of the computational part of the projects. Not just WCG but actually F@H, Rosetta@home, and CPDN are such platforms.
2.) From the volunteers' side, one related question would be: Is desktop computing dying out? Of course, several DC projects adopted mobile computing too, including computing on telephones. But let's face it, the form factors imply that desktop computers and occasional compute servers are doing the bulk of the work in DC.
As others already mentioned, the cost of electricity has obviously become more of a concern for the typical DC volunteer demographic in recent years, not to mention most recent years and months. I suspect this does not only cut into how many households take part in volunteer based DC, but it especially might cause fewer and fewer corporations and publicly funded organizations to be willing to donate computer time to DC.