Amazon CloudFront seems to have this feature since 2013 for free.
Would be nice to have it in CloudFlare too.
I have an idea for a low-budget service where I want to use Cloudflare Workers on all unregistred subdomains to output a page customized according to the subdomain name.
Because the project is just an idea and budget is low I can’t afford myself acquiring an Enterprise plan or even Pro.
A further abstraction of the project idea would be allowing users to bring their own domains to the service and manage them but as CloudFlare plans are per domain I doubt it will be feasible, without Enterprise plan at least.
Have you thought to start providing static site hosting service with CF? Maybe in partnership with Netlify.