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“any media outlet, no matter how big an empire it is, that is not owned or funded by the state” is not the common definition of “independent media” (it’s not even the definition given in the hyperlinked definition). “Independence” in this context refers to journalistic independence.
Ignoring that it would be impossible to implement on an infinitely-diverse-in-infinite-combinations fediverse, I think we can all agree this “feature” would not be getting many upvotes if people didn’t feel a need (boredom or otherwise) to browse “All”. The real “issue” is not enough “apolitical” content for them (fwiw I disagree but that’s another topic).
“Stuff in my feed I don’t want to see in my feed” is kind of the exact problem the Fediverse set out to solve. Nothing gets “injected” to a feed here so if you are seeing it, it’s a choice to continue to do so.