I think we should focus on ideas that REPAIR the current state of the AM band, instead of looking towards the Internet. For starters, rescind HD operation on the AM band; too much splatter into adjacent channels, not to mention background hiss on the main analog channel. Next, rescind permission for all those daytimers who operate at night with super powers of 5000 milliwatts or so. And, since Canada turned off a good many of its AM stations (yes, they migrated to FM), allow those stateside operators who were protecting Canadian AMs to alter their directional patterns. Granted, this cannot happen overnight, but should be among those ideas considered by anyone serious about saving AM.
If, OTOH, you want a quick solution, or want to throw in the towel re noise/interference from computers et al, just tell the public that all AM transmitters will be turned off on some future date, and everything formerly on-the-air will be moving to the Internet. Let me know how well that works out.