The inability to build starships to meet the demand, any demand, is built into the very structure of Trek drama. Otherwise how could Starfleet always be so starved of ships that the heroes arrive at or after the nick of time, when just adding a thousand ships would make the colonies safe?
They don't need sleep or food
To be accurate, we don't really know that. We know the White keeps them going, possibly for days at an end, and we know they refuse to sleep or eat during a mission. But they do have digestive systems, and they do seek and consume food in "Hippocratic Oath".