The role of timestamp
The timestamp is used primarily for establishing the difficulty. Without a timestamp, new nodes would not be able to determine the correct difficulty to be used for each 2016 block period as they wouldn't know how long it took to mine those blocks. So that everyone calculates the difficulty correctly, the block timestamps are used instead of real time. 

This of course means that the difficulty can be manipulated by miners messing with the timestamp, but nodes do still check them against real time and will ignore blocks that are outside of a certain range of times based on its own internal clock time.