Something that has not been brought up in this excellent string of comments is the cost of operation. A small rural AM, especially a non-directional one, is much less costly to operate than one in or near a major metro. For example, the price of land alone can dictate more about what format choices you will utilize based on how much potential revenue is available.
A station I worked for upgraded. Their once very rural location was being swallowed up by big box stores and new subdivisions. The station moved about 25 miles further from the big city. They sold the once rural tower site which produced enough revenue to increase power to 25,000 at the new location, the total build out including all new equipment and still left a little pocket change. Even so, the land wasn't cheap and nor was the operation. It was easily 2.5 times what a small town station runs and that was so bare bones it was pathetic.
Many asked me why we didn't do oldies or some other format on that big city AM and hire some once household names to jock it. The truth was the promotional dollars to build awareness of the station, the cost of operation including salespeople to work the slim pickings of mom and pop businesses that did not have an advertising agency running their buys, I could have easily eclipsed $1 million out the door in under a year. It would be impossible to ever bill enough to repay the initial investment. I'd need a good 500 regular advertisers that tended to average a budget of $200 a month to make it without thinking about the 'ramp up costs'. The issue was, even with good promotion, the number of listeners in the trade area of the average single location business was so low that advertisers rarely saw any results and generally never renewed their advertising. I had worked such a situation where the cost to acquire an advertiser was about what that advertiser could spend. In other words, you worked your tail end off to not make any money and the station had to foot the cost of the operation and jocks in addition. At minimum, I'd need about $100,000 a month to break even on a shoestring operation. If I ever could get there monetarily, you can bet there would be a competitor that would steal the format and slice that pie in two. And if that was a big boy, I would be forced to go back to square one, spend another million on some other format and try to make the money back. That's the major market scenario. The best way to survive the major market as an AM standalone is by flying under the radar appearing not to be too successful to call attention from hungry competitors.
Meanwhile, in the small market rural station where land is cheap and your coverage likely not several counties, it is easy to make things work by comparison. First, populations tend to be older. Second, hardly anybody uses ad agencies, so you develop a relationship in person with local business owners. They spend about what the major market mom and pop can afford. Promotion is a breeze since there are very few media outlets and most are eager to cross-promote. I can likely find a few local people to sell on a part time basis to people they may have known all their life. I might need $8,000 to $10,000 a month so 40 or 50 clients at $200 a month can be had if you work on it. Plus you can sell community events and school sports/activities. Almost every business wants to buy graduation salutations for high school grads or buy that Christmas Greeting in December. Literally in a small rural spot each can represent about an average month's billing in extra revenue. Here ads are sold more on relationship and the business buying to demonstrate they are a part of the community.
So, to answer the question how a small rural AM can do it but a major market station, even at the birthplace of the music, likely cannot make it work, it all boils down to cost from land value to building awareness to sales potential.