Why was it important for the people of Vedic Age to write down their history?

Because they wanted to Record the rules and trade that was being brought

For many years, the people shared ideas and thoughts orally, or by word of mouth. They then used Sanskrit to write down poems, hymns, and other religious ideas. One of the most famous poems ever written was the Bhagavad Gita. Bhagavad was a supreme god and gita means song. So Bhagavad Gita means "The Song of God." So writing down their history made it easier in different matters.