This is now fixed here Now it will use desktop logo if the small logo is not available.
https://github.com/discourse/discourse/commit/6b818fb855e7520f44e2fac2ebe7353d8f2f3357
I think we should use site title if both logos are not available. But in the current UI, it looks not good since we have page title next to it. Maybe we should move page title from the site header like in the below examples?