This may be true with some, but it is not true of Fastly. Each of their edge nodes is a varnish cache. Because they are multi-tenant, when varnish crashes it crashes hard and takes everyone with it.
The question in various threads is why not have redundancy -- but the point of a CDN is to have extra servers and capacity and lots of locations to make individual crashes just flow elsewhere.
But if the single customer with a valid-yet-crashable config had lots of traffic all over the world... it'll take everything out at once.
Redundancy of CDN is more expensive, and still requires DNS failover. People do the calculation and usually decide that 30 min of downtime every couple years is worth the saving on vendors and code and hassle. They don't like it, but every site that was down made that decision.
They frequently have a common caching servers located close by. so maybe every 10 or 100 edge locations have a single cache location.
Edge is a reverse proxy and probably handles ssl handshakes. So if your cache is down, all your edge locations in that area are down