My machine (Cuisinart) has both a timer and a warmer-timer... I always set the timer, but on the weekend I may or may not sleep longer than expected. I don't want my coffee sitting on a hotplate longer than about 5-10 minutes. In the summertime, I usually make iced coffee anyway, so there's no need to reheat.
I only make enough for one morning's worth... anything that IS 'left over' would only be the 'silt' at the bottom of the carafe... and sometimes, when I really need a bit of a jolt, yeah, I'll drink that stuff, too.