In practice this works only for trivial apps, that have no dynamic content, don't serve large files, don't see a lot of traffic, doesn't come from all over the world (each PoP has a separate cache), etc.
True, but this means your solution is competing with Github pages, Netlify, etc. and your visitors are still subject to the whim of the caching layer. I'm not aware of any classical CDN product that works Great even when the origin server doesn't. Building a CDN for that purpose only would be extremely niche - generic CDNs with a hand-tuned caching policy are great at many other things, such as live video delivery, so you'd be building a non-generic CDN in a saturated market. Then the question of how does the CDN make itself aware of the content it needs to prefetch... once you devolve into that, well you've reinvented git push to Netlify, but with 10x the amount of quirks, oddball architecture, and less flexibility.
So something exactly like a blog then.