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. CDN caching is opportunistic, most services assume server-grade hardware at the origin that can take some "warmup" load on its own.
Also if you're introducing a third-party CDN/cache, you're already throwing away a whole bunch of reasons for self-hosting in the first place.
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.
If you're building something as complex and convoluted as a blog hosted on a smartphone being tunnelled to the outside world and proxied through a purpose-built CDN, I don't think you can call it a website anymore.
I'm not pushing anything, just haven't seen pass-through proxy that has a similar failure mechanism for when websites are down. They have enough of a market share without me promoting them anyway.
That's a feature of basically any CDN and some existed well before Cloudflare entered the market.
Nowadays you find dozen of CDNs. A personal site may be fine without it. If your plan is having an offline version ready to be served, as you expect a lot of downtime, distributed cache might not be the best architecture. Some CDN offer a dedicated layer of cache in front of your origin, but that sounds overkill for a personal blog.
At that point I'm not sure if it's functionally different to syncing markdown files to something like S3 or GitHub pages.