[…] I’m not concerned with who is doing the work, I’m concerned with the amount of work involved and how practical it is for every one of us to do it as a matter of course every time we access information online.

The only impracticality that I can currently see is the example that you gave earlier ^[1]

[…] I presume we don’t want every private citizen to be making phone calls to verify every claim they come across in social media […]

But just because it may not be practical for an average person to verify a source in all cases doesn’t feel like a valid argument for why sources (that the news outlet has already verified) shouldn’t be provided. Say a news article is reporting on a claim that an interviewee made in an interview that they conducted. Say that the interview interview footage is posted on its own. If the news article is commenting on a claim being made by the interviewee, is there any reason why the interview shouldn’t simply be directly cited? It would remove a lot of burden from the reader if all they have to do is click on the link to the video and scrub to the timestamp to hear the claim for themselves. Yes it would be impractical for each reader to contact the interviewee for themselves to verify that the interviewee did actually say that; however, I think that it sometimes is less about a skepticism of reality, but more a skepticism of reporting bias.