The real position of the living entity is to become the servant of God, but because Lord Krishna happily became the servant of Arjuna. Arjuna was sitting on the chariot, and Krishna was working as his driver. Krishna felt obliged because Arjuna had a pure, transcendental friendship with Him. The Lord is so merciful that He related to His devotee, Arjuna, just like a friend.
Srila Prabhupada once explained that when Krishna is fighting as Arjuna's charioteer, His pleasure potency, Radharani, is there, but is not manifest. It is not that when Krishna is Parth-sarathi, Radha is out of Him.