Rankings exist; a widespread one is the Press Freedom Index from Reporters Without Borders. If you check the 2021 ratings on the map¹, you will see that excellence is reserved to a few countries only - CostaRica, Portugal and Ireland fare better than the UK, France, Germany, the USA and Australia.
With "receiving public funding yet not reaching thresholds of quality for public use" it was meant that if the news organization receives public funding, its quality should reach some level well above that of an agency financially left to its own devices, and its quality should justify public investment. An entity receiving public funding is supposed to respond about its use - practices, outcomes etc.
¹ https://en.wikipedia.org/wiki/File:Press_freedom_2021.svg
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Now: the poster seemed to indicate a relation between "market" (number of buyers) and quality. The idea that information, commentary, analysis and research results and validation can be made akin to a "deregulated and for profit industry" (e.g. the music industry) is perplexing. Bread and water - privatized or not - must be accessible and not toxic, as part of societal organization. Less buyers' funding does not imply quality decrease, and free access to vital parts of knowledge is public concern.
The Press Freedom Index ranks countries media landscapes, not newspapers. Therefore, it cannot be used to allocate funding. We can use it to bring awareness to failings in public policy in particular countries.
I did not indicate a relationship between market and quality; on the contrary, I attempted to repudiate such a notion through a reductio ad absurdam.
How do we measure quality? How can we prevent those who benefit from poor quality media, once in power, from tweaking the measurements to give it to their supporters. That is my question.