It doesn't. I only need OS 10.9 or later and I have 10.12.5. So I maybe should go straight to the App store and then to Catalina.
According to
macOS Catalina - Technical Specifications, you're correct about needing only OS X 10.9, so I don't see any reason why not.
Recovery is really a sort of emergency tool and isn't meant to replace the regular upgrade process.
How to upgrade to macOS Catalina directs you to a Catalina d/l in item 4.
More: It may be that you need 10.12.6 before Software Update kicks in, but it's apparently not a technical necessity for installation.
