Is rice supposed to be eaten with chopsticks?
The Chinese cultural norm is to eat rice with chopsticks. It would be very inconvenient to constantly switch back and forth between eating with chopsticks and a spoon depending upon whether you were eating rice or vegetables or meat. 

To get around the loose grain problem, you can use the shovel method. You pick up your bowl and use a shoveling motion with your chopsticks to eat. 

This video illustrates the shovel method as well as picking up clumps of rice.