One other thing the overflow tank does is replace air in the system with coolant. Short of pulling a complete vacuum on the system and then filling it with coolant it is hard to get all the air out when doing an initial fill.

In use, the air in the system will make it's way to the radiator cap area and vent out the cap as the system heats. When the system cools and makes a vacuum the overflow tank supplies coolant to top off the radiator instead of allow the system to suck in air.