When a SHTF or TEOTWAWKI event happens, millions won't be prepared, AM radio or no AM radio.
You can try to persuade people to have some sort of preparedness, including communications preparedness, but you can't force them. This is one reason why FEMA estimated that 90% of the US population would be dead within a year or two of a major EMP event.
So, let's suppose that there were more AM radios in houses, or even stuffed inside a cell phone. Lets assume that an AM band-based emergency notification system worked. That doesn't mean that it would be used, any more than any other system, or any other form of disaster preparedness on the part of the general public. Any governmental attempts to inform the population to be prepared for adverse events is going to fall on deaf ears. It's just the way it is.
Even our nation's (and the world's, arguably) health care system wasn't prepared for a pandemic -- even after warnings by major influencers like Bill Gates concerning the potential for one, and previous scares like the Swine Flu epidemic, or SARS. My public, tax-supported hospital district was like most others in the region in 2020 -- virtually devoid of personal protection equipment when corona hit. They all apparently thought there would never be a need for it. And for the first 50 years the hospital district existed, that was indeed the case. No need. So, hey -- no worries.
In that respect they were no different than your average 9 to 5'er -- living day to day, blissfully unaware and -- for the most part -- serenely oblivious to the potential hazards that could strike at any moment. Maybe for good reason.