I'm kinda surprised that "newsstand" isn't a popular payment strategy. You just have an account with WaPo and when you want to read the paper you pay $1.50 and get the "digital print edition" which has all the articles published today organized into neat little sections.
Newspapers don't have to become Spotify; iTunes is also good.
But even with the newsstand model, you could always subscribe and have it delivered (usually at a discount vs the news stand).
The publishers (and lots of other busineses, think fusion360/photoshop/etc) are just greedy, they can't see the value in thousands of people randomly selecting their product today, and their competitors product tomorrow. They want lock in because its easier.
Newspapers don't have to become Spotify; iTunes is also good.