Prime has an estimated 10 million members. Providing a Post subscription would probably sell more Prime memberships. Going by numbers I’ve seen quoted about the NYTimes (see http://www.businessinsider.com/new-york-times-print-versus-online-2011-5 ), a print subscriber is worth ~$385 per year in advertising alone.
I would assume that the ~$385 in additional advertising Amazon could sell, would cover the cost of sending every Prime Subscriber a “free” copy of WaPo.
Why would that be attractive to Bezos?
Don’t forget, Amazon is working very hard on improving the speed of delivery to the home and bringing down delivery costs is a byproduct of scale. If they’re already coming to your house every day, then delivering another product quickly at the same time, can only improve margins.
Of course, a big question comes up. Is this feasible considering Bezos bought WaPo personally? I don’t know.