ALL power plants require external power for cooling once they're tripped. In big plants like that, if you don't shut the system down correctly and cool the boiler off in a controlled fashion, you're going to cause all kinds of damage. This can include catastrophic failure of the boiler. Only difference is a coal fired boiler doesn't contain nuclear fuel and radioisotopes.
Fukushima was a cluster fuck. American plants apparently have more redundancy on the emergency generators than Japan requires. In addition, there are emergency cooling systems, even in the older designs, that use (for example) the steam generated by the plant itself to turn pumps. In Japan, they'd never tested those systems; so, didn't know if they were working or not (they were not).
I would like to see the plants all upgraded to newer designs myself but that's going to take decades; and, in the current societal and political climate may not happen.
The trouble with doing something right the first time is that nobody appreciates how difficult it was.