It all depends on the use-case/context. Hosting a single video with few concurrent views is cheaper to do on VPS. Hosting videos with short response time in any region, with high resiliency, etc. is likely cheaper to do on CDNs. It's not a myth. It's "general advice may not work for you".
Not sure what you mean by false advertisement. Australia-Netherlands (common European pop) connection is often >300ms from a home connection. Home in Australia to Sydney pop is likely <10ms. It makes a massive difference with many small resources, or restarted transfers. That's just physics at some point.
But does it really? I can see why a large company wants to squeeze milliseconds out of asset delivery, but as a watcher of a small independent creator I would have no problem waiting a second for the video to start playing.
Latency directly impacts bandwidth, which impacts quality, since all current-gen user-facing live streaming protocols that matter (HLS, DASH) are layered on top of HTTP (on top of TCP), and that's already the best trade-off for end-user delivery today.
For VOD it's less of an issue since you can just maintain a larger buffer, but with live that's a trade-off with being closer to the live edge or choosing poorer quality. It works OK for some cases, it's bad for others (like sports, or when letters on the screen become illegible due to compression artifacts).
Building your own CDN off of el cheapo VPSs is theoretically viable, the beauty of HLS and DASH is they're 100% plain old HTTP, so just drop Varnish, add GeoDNS on route53 and off you go. Actually I'd love to have the time to try that :)
Here, the roundtrip latency is ~14ms within the country (e.g. from here to capital city), and 40ms to the closest AWS or GCP datacenters (both are in Frankfurt).
