The Godhead is not dependent on His worshipper [for His benefit]. Asvādhīnam and svādhīnam also indicate that the Godhead did not order Him [to do anything but Rāma’s father] did order Him [to go to the forest].

NOTE. While this is a general scriptural rule, there is the following scriptural exception to this rule:

devarṣi-bhūtāpta-nṛṇāṁ pitṝṇāṁ
na kiṅkaro nāyam ṛṇī ca rājan
sarvātmanā yaḥ śaraṇaṁ śaraṇyaṁ
gato mukundaṁ parihṛtya kartam

“One who has given up all material duties and taken full shelter at the lotus feet of Mukunda, who gives shelter to all, is not indebted to the demigods, great sages, ordinary living beings, relatives, friends, mankind or even his forefathers who have passed away.” (Śrīmad-Bhāgavatam 11.5.41)

The meaning of this Bhāgavatam verse is clarified in the Caitanya-caritāmṛta as follows:

kāma tyaji’ kṛṣṇa bhaje śāstra-ājñā māni’
deva-ṛṣi-pitrādikera kabhu nahe ṛṇī

“If a person gives up all material desires and completely engages in the transcendental loving service of Kṛṣṇa, as enjoined in the revealed scriptures, he is never indebted to the demigods, sages or forefathers.” (Caitanya-caritāmṛta Madhya 22.140)

Right now, Lord Rāma is teaching us how to follow the general rule.