Why can't coolant dry inside the engine during engine operation?
The cooling system is sealed and pressurized, so under ideal conditions, nothing goes in or out. "Drying" is simply evaporation followed by the carrying away of the evaporated water by air.
In reality, there is a slight opportunity for evaporation out of the overflow tank, which is not sealed/pressurized on many vehicles, but as the coolant in there is much cooler and there are no large holes, the rate of loss will be very very low.
The cooling system uses pressure to further raise the boiling point of the coolant. Just as the boiling temperature of water is higher in a pressure cooker, the boiling temperature of coolant is higher if you pressurize the system. Most cars have a pressure limit of 14 to 15 pounds per square inch (psi), which raises the boiling point another 45 F (25 C) so the coolant can withstand the high temperatures.