Some background as to why WLW had a 500,000 watt transmitter...
Between 1934 and 1942, WLW Cincinnati was given FCC permission to run half a million watts. Its owner at the time, Powel Crosley, Jr., was a strong supporter of President Franklin Roosevelt and got special FCC approval to boost its power. Crosley was a manufacturer of radios, refrigerators, even a car called the Cosleymobile. He had first put a station on the air in Cincinnati in 1921 running only 20 watts. Over time, he kept increasing the wattage. In 1934 he spent half a million dollars (today nearly $9 million) to construct the giant transmitter. Pres. Roosevelt was given the honor of pushing the button turning on the half million watts.
At the time, there was no other station on 700 in all 48 states. But with such high power, stations on nearby frequencies complained, even one in Toronto. For a short time, WLW powered down to 50,000 watts at night. Crosley constructed two more towers to make WLW directional, away from Canada, and resumed 24 hour operation at 500,000 watts.
In 1938, under pressure from other broadcasters that didn't have superpower authorization, Congress passed the Wheeler Resolution, suggesting AM stations not exceed 50,000 watts. The following year, Crosley lost his special superpower FCC approval. In 1939, WLW returned to 50 kW, non-directional.
Today, the maximum power for all U.S. AM stations licensed by the FCC is 50,000 watts, although 1170 Radio Marti in Marathon FL, not under FCC jurisdiction, operates at 100,000 watts, directional to Cuba. Mexico has about a dozen stations running more than 50,000 watts, with 900 XEW Mexico City grandfathered at 250,000 watts.