Lots of folks don't know that coal and gas fired plants are able to turn down their power generation more than 90% (i.e., "ten to one turn down"). It's definitely true that cold restarts take a while. However, they often rather quickly and dramatically change their power output profile while running.
I don't doubt there's a small number of plants that can't do 10-1. That said, transmitters are intended to be replaced and upgraded regularly since they have a finite lifespan (they're cheap anyhow). 10-1 has been around for 35+ years now and you're really lucky to get 20 years out of a transmitter.
I know of one factory that has their own coal power plant. The boiler is from the 1880s, the generator installed in the 1920s. It is horribly inefficient by any reasonable standard and takes hours to turn on. However because they keep it operational the power company gives them a massive discount on electric. About ever 5 years there is a major event and the power company has them turn it on for a few days and they power the entire town.
A transmitter is a sensor in a power plant that very precisely measures the air flow within the combustion chamber, so the fuel burns as clean/efficiently as possible. Relatively new transmitters can read with more precision, so you can dial down the airflow/fuel and the corresponding power output.