Update 9/19: As if on cue comes this article about the FCC Chairman's recent comments on how to rejuvenate broadcast AM. Yes, this proposed new arrangement of deck chairs should really help with the buoyancy issues, never mind the icebergs and that inconvenient gash in the hull.
In a tab-clearing exercise, I direct you to an article at the NYT, A Quest to Save AM Before It's Lost in the Static. Go read, it's short, I'll wait.
Daytime groundwave & nighttime skywave MW coverage, from broadcast AM article at Wikipedia.
NB: amplitude modulation and medium wave spectrum are not inextricably linked. You can have AM in other parts of the electromagnetic spectrum (e.g., CB radio), and you can modulate in the MW spectrum using other modes, such as digital encoding. (Confused? Then re-read the second paragraph.)
Digital modes used to be NASAspensive, but in these days of $3 DSP chips cost is not the show-stopper it once was. But digital modes have their own set of problems. A hybrid AM/digital scheme tried in the U.S. had severe problems and has been pretty well rejected, while pure digital systems are not permitted. Yet.
The regional aspect is perhaps broadcast AM's strongest point. But even this capability is no longer unique, with the advent of internet and satellite radio. AM's still unique in that it combines regional with free and robust, and that does make it still the king of emergency broadcasting. Which is really nice, speaking as someone who went through a wide-reaching blackout in Katrina, but relying on emergency broadcasting revenues isn't a viable business model.
As for Mr. Pai's localism argument, conventional FM broadcasters do quite well (even the most powerful FM stations can only radiate to about 50 miles, it's limited by the Earth's curvature), and the new class of low-power FM stations is increasingly filling the ultra-local niche.
So what is left for broadcast AM radio? Regional nighttime broadcasting for the commercial purposes listed above, and then especially for emergency broacasts. A someday-hope of a workable digital system. And a huge installed base of transmitters and receivers.
What's in the future? My guess is that things will totter onward as-is for maybe a decade more, as legacy equipment and legacy users fade away. After that, AM will be down to a few threadbare broadcasters scrapping over a 5% radio market share. From there, I'm guessing we'll see a change in regulations to allow pure digital modes. FEMA might step in to buy up and preserve a few high-powered stations for emergency regional broadcasts in plain old amplitude modulation. I'm guessing it'll be some combo of these two.
AM's MW spectrum is too cool of a resource to just let lay there and go to waste. But all of its weird legacy, quirky propagation properties, and a public that has become unaccustomed to using it are going to make rough going for a few decades. In the meantime, I'm going to go have a cold beer and listen to Eddie Stubbs spin records (yes, actual vinyl in many cases) on WSM.