On the other hand, in summaries for a broad readership, the posteriors are the most important result to report. Now most readers don't have the expertise to bring their own priors, so you have to give them yours. And then do the calculation for them.

Good point. It would be irresponsible to publish a news item that "the Prime Minister's support for this bill is three times more likely if he is, in fact, a lizard alien than if he is a human" without noting that the prior probability for him being a lizard alien is pretty low.