The information on the card simplifies the system by making easier for selective service applicants to be in contact with the selective service boards. The ability to communicate allows the government to call up individuals for military service, which is of vital interest to Congress.
Draft cards can be illegally changed or modified. Destroying the cards entirely makes it almost impossible to catch the people who attempt to dodge the draft by altering them. This significantly inhibits the interest of Congress in creating a military very quickly to respond to threats.
The information on the draft card still serves a compelling interest to the government as showing the card to an official upon request quickly helps ensure its bearer is following his selective service requirements.