IMHO, I think it's mostly a solution in search of a problem. The internet backbone is fast enough to not be noticeable for end users. A centrally located server in the U.S. will have a maximum ping of 40 ms to anywhere in the U.S. That's faster than is perceptible to the end user. The only mainstream usage I can see is cloud gaming where ping is that critical.
Establishing a connection can require several round trips, and the latency adds up. "early termination" with a point of presence near your end user makes a pretty massive difference, especially if your user isn't on the same continent. Every additional 100ms costs amazon 1% of their revenue https://news.ycombinator.com/item?id=273900
I agree, I've been looking at discussion one here recently on how someone was working on the problem of "data storage at the edge" to compliment their "compute at the edge" offering. I think you can argue that that when you move compute and data storage to the edge you've effectively moved the data center to the edge. At some point if you put enough data at the edge you operating your own backbone makes economic sense and CDN don't maintain backbones they mostly buy paid peering and transit and try to leverage public peering wherever they can. I would even say edge compute is a solution in search of revenue stream and hedge in a heavily commoditized market.
(2) You can achieve 100-130 ms latency with a "like one data center per continent" sort of network. You don't need edge computing on hundreds or thousands of edge sites to achieve that.