Firstly, it was never said that Rama is the ONLY one who had followed father’s words. But he is one of the first ones who has excelled and stood as an example for the way a son should respect and obey the father. In fact, Dasaratha, Rama’s father could not order in words that Rama has to go into forests for fourteen years. But, Rama understood the situation of his father and the thoughts in his heart and followed the unsaid words. This is the greatness of Rama.
When Bharatha approached Rama and began to plead him to come back to kingdom, Rama refused. Bharatha even said to Rama, ‘Dear brother, Father has given me the kingdom. Now that the kingdom is in my hands, I would like to give it to you. Let me go to the forests’. Rama answered, ‘Father is no longer here to change his order. We are not authorised to exchange/alter/edit his wish. Let us just follow father’s words.’
– From the ‘Q&A Session’ with Sri Chinna Jeeyar Swamiji, Ramayana Tarangini, 2017