You don't need it, but is helps a lot with thermal conductivity from cpu to heatsink. Between cpu and heatsink without thermal paste is thin layer of air and air is known for its isolating properties, thermal paste gets rid of this air. You can reuse old paste, but most of time it is either too dry or unevenly spread so placing cooler back will create trapped air bubbles. So it is recommended to clean old paste and apply new one.