" But Bhagavath Gita is not written by any sage, but spoken by God himself."

That is just your opinion, Vaishnavas may believe that also, but other Hindus believe the Gita was writen by Sage Vyasa or many Sage(s) which is just another Upanishad and is not the word of God. If you believe the Gita to be spoken by the historical Krishna himself, where is your proof? Historians research found that it was written between 500-300BC, not around 3000BC.

The Vedas say little about Lord Vishnu, which is surprising if he is supposed to be the supreme God.