Arjuna was also a pure devotee, but he never chanted neither did Krishna asked him to do so. So why do you stress so much on the same?
Chanting the name of Krishna means to constantly remember Him. Although it may appear that Arjuna was not chanting like we chant on the beads, he was calling Him in great eagerness by different names like ‘O Yadava, O Keshava, O Madhava’. This is certainly a sign of great advancement. He was put in such an awkward situation by the will of Krishna that he had no other choice but to call out in great desperation.
The dealings between Arjuna and Krishna were under Krishna’s internal energy, however we are affected by Krishna’s external energy. In the beginning we do not have taste for the Holy Name, therefore we are asked to chant in a prescribed way. Therefore we stress on chanting so that we come to higher level, wherein we are able to chant in great eagerness.