I think it's not good for the coffee machine to keep the coffee warm. Coffee that has been kept warm for hours tastes awful. It's better to let it cool down, then warm it in a microwave when you want to drink it. If I've had enough coffee for the day and there is some left in the pot, I save it in the fridge for the next day, then re-heat it. Its flavor is not snob quality after that, but it's better than keeping it hot for that long.
Cheap coffee makers have a single heater that heats both the water and the hot plate. Since the water needs to be brought to a boil, the heater's thermostat needs to be above boiling, so the hot plate will also eventually hit boiling, which is really bad for the coffee.
Coffee machines usually don't boil the water. They heat it enough that there is some evaporation and the vapor pressure pushes the hot water through the drip mechanism. It is well below boiling, like maybe 170 or 180 F, and one of the complaints about cheap machines is that they don't get the water hot enough.
The issue of coffee tasting bad if kept hot too long is independent of the brewing method though. I generally make coffee manually (pour hot water over a drip cone) and it is an issue then too. I stopped using a thermal carafe because of it.
