And it makes sense for the label to be applied specifically to media entities because journalists are supposed to be unbiased, as opposed to e.g. Raytheon which is objectively state-affiliated but nobody expects to be doing objective reporting.
If a media outlet is being funded by the government then readers should know that because it could affect their coverage if they fear losing that funding as a result of critical reporting. This directly applies to NPR because Republicans regularly threaten to remove its public funding in response to their coverage.
The better criticism is, why is the label applied to NPR but not e.g. MSNBC? Pretty sure at least Comcast (MSNBC's parent company) receives a significant amount of government funding.
This has never been the case. Never. While some journalism sources operate in a facts-only manner, all journalistic sources have bias as to which stories they research. And historically, the press has been about propaganda, editorials, and selling papers at least as much as about reporting.
Labeling news organization as "government-funded" is less informative than labeling them as "propaganda" or "editorializing". The major reason to so label them is, itself, propaganda. With the second reason being a warning to the reader to practice even more diligence than normal.
By your own reasoning, those other labels would be redundant. Whereas "government-affiliated" makes the reader aware of a specific kind of bias that not all media entities are subject to.
close, if there is evidence their coverage is actually being affected, readers should know that because that is what should inform their decision
in some cases, where the funding constitutes a large portion of total funding, it may be appropriate to add a disclaimer
Meanwhile case-specific evidence is largely unavailable. Reporters would be loathe to admit to being cowed, but are also aware that corporate executives make decisions on things like promotions and timeslots based on the bottom line, or in less well-funded entities that a loss of funding can directly lead to a loss of employment.
How about statistical evidence? Well, if Republicans are threatening NPR with the loss of funding, they could slant their coverage to placate the legislators criticizing them, or they could slant it the other way to bolster their support from the other party. In either case it compromises their neutrality, but now you can find "evidence" of this in any divergence from neutrality in either direction. Since they couldn't reasonably be expected to be infallible in the alternative, that doesn't prove anything.
So you make people aware of the incentive, because that's all you're really going to know about in practice.
Ad Fontes tries to rate news media on the type of reporting it does and the general political skew. This doesn't capture everything, but it can be done. Except for specific topics I think it's slightly better than incentives in general, though incentives are important too.
an example of evidence of such a conspiracy theory would be internal emails telling a reporter to go easy on the US government because a small portion of funding comes from it, or to attack X because the US government wants them to
statistical evidence would work too if it proves the claims of bias somehow, I leave it to you to figure out some examples
And social media companies are more like convenience stores that also carry newspapers. The large majority of tweets are not by media outlets.
Clair Cameron Patterson famously took money from the leaded gasoline industry to help fund his research demonstrating the harms of leaded gasoline.