If there was to be a major disaster in my neck of the woods - there is nothing out there to educate the public to tune to the city's major news/talker.
But let's get real. No one is gonna depend on a battery powered AM radio in the dark waiting for the government to tell them what to do. Frankly, the last person I'm going to trust my life to is someone from the government.
Most people have the wherewithal to figure it out on their own. I got a generator, firewood, food and fuel to get me through a few days. If it's so bad that I gotta bug out - I have a new Subaru with AWD and friends/family who live within an hour's drive. If worse comes to worse, I have enough guns and ammunition to take what I need.
If said disaster was to knock out that major 50kw news/talk AM station - then what? Where do we go next?
AM radio is a dying breed. Smaller / local stations are going dark. Larger stations are all automated corporate rebroadcasters with actual on-air people voice tracking from home 6 states away. You may have 2-3 actual live local voices who come in to do the morning and afternoon news - but they're also doing remote/voice work for other corporate stations too. As for getting out breaking doomsday news - this assumes that the station is physically or remotely accessible. The AM highway travel info stations are all gone here in NY.
I rarely use the AM/FM function of my car's entertainment center. It's usually whatever streaming service I'm listening to via Android Auto. If I am tuning into a local station to listen to the news - it's on their FM simulcast. Maaaaaybe I'll go to the AM version if the FM station is out of range - but that's rare... they have a phone app for that. If AM disappeared from my dashboard, I won't miss it.
Now in a real shit hits the fan scenario - I live in one of the (if not THE) most disaster free part of the US. So bad days are exceptionally rare for us. I know what the major AM news/talk station here is. Other AM stations - couldn't tell you who's what. Hit 'scan' and hope for the best - and odds are it's playing some satellite fed syndicated programming anyway. But between home internet, 4G/5G, AM, FM, OTA TV - something will work for most people.
Keep this in mind - unless you live in Florida or along the Gulf Coast during hurricane season and are in the path of a CAT 4 or 5 hurricane, most natural disasters are fairly localized in nature. The worst ones I've been through was Hurricane Gloria on Long Island in 1985 - power was back in several days, an ice storm in upstate NY in 1991 where the region lost power in places for up to 2 weeks (we were back on within 36 hours) and while that got tough for some people - they got through it. We had the big power outage in 2003 in the northeast but power was back in later that evening. I honestly don't recall any widespread suffering or agony. People got through it. TV/AM/FM radio stations largely stayed on the air. Landline telephones mostly worked.