C2 is better than the language proficiency of the median native speaker.

A C2 speaker is comparable to a highly educated native speaker with a master degree who reads regularly.

If a native speaker didn't pass a C2 exam, it's not because they don't understand the language well enough, it's because they are bad at reading/writing as a skill and might make e.g. spelling mistakes.

Any native speaker will still be far beyond C2 when it comes to intuitively understanding a language and using it. No native speaker will ever fail the oral part of a C2 exam, unless they have to talk about a topic they don't know, which would be a case of a lack of knowledge, not a lack of language proficiency.