Reference: Balakanda 8th Sarga Why did Dasharatha propose performance of Ashwamedha to beget children? Ashwamedha is primarily to establish supremacy over other kings. I am unable to understand the logic or dharma behind this.
I am quoting my friend Sri Kiron Krishnan's answer here, on Aswamedha in other site, to explain the meaning of the same as per Vedic mantras. According to Vedic sense, Aswamedha should be viewed in an esoteric manner only, but not physical sacrifice of Aswa or Horse.
By the time Ramayana was composed, please do not get confused with the period of occurrence of Ramayana, this got degenerated to physical sacrifice. However, it was being done in the times of King Dasaratha to beget sons only, but not for establishing supremacy over others.
King Dasaratha proposes to perform Horse sacrifice for begetting sons, as he was not having sons.
मम लालप्यमानस्य सुतार्थं नास्ति वै सुखम् | तदर्थं हयमेधेन यक्ष्यामीति मतिर्मम || १-८-८
"My mind is tumultuous without quietude for I have no sons... for that reason, I wish perform Aswamedha, Vedic Horse Ritual... this is my thinking.
By the time Mahabharata was composed, the purpose of Aswamedha had become to purify one.
Yudhishthira replied, 'Beyond a doubt, the Horse-sacrifice purifieth princes.
The Horse in Mahabharata period was released for conquering other kings, and to display the glory of Yudhisthira.
"Vyasa said, 'Myself, O son of Kunti, and Paila and Yajnavalkya, shall without doubt, achieve every rite at the proper time. The rite of initiating thee will be performed on the day of full moon belonging to the month of Chaitra. Let all the necessaries of the sacrifice, O foremost of men, be got ready.
Let Sutas well-versed in the science of horses, and let Brahmanas also possessed of the same lore, select, after examination, a worthy horse in order that thy sacrifice maybe completed. Loosening the animal according to the injunctions of the scriptures, let him wander over the whole Earth with her belt of seas, displaying thy blazing glory, O king!'
You're right. Conducting an Aśvamedha simply to beget sons is both unnecessary and extravagant.
As Robert P. Goldman says in the Introduction to his translation of Bālakāṇḍa, in all of the Aśvamedha yajñas from both the epics combined, no king besides Daśaratha has performed it for getting sons so it must be a late addition to the text:
The saga of the Rāmāyaṇa begins, as Jacobi claimed, with the fifth sarga of the Bālakāṇḍa in which the audience is introduced to the royal house of Ikṣvāku, its scion King Daśaratha, and its hereditary seat Ayodhyā, capital of the fair realm of Kosala. Sargas 5-7 describe in some detail the glories of the city and the surpassing virtues of its inhabitants. The descriptions are elaborate and extremely hyperbolic, but this is in keeping with the style of the Sanskrit epics and lends weight to the Rāmāyaṇa's claim of universal sovereignty for the princes of the Rāghava line.
Daśaratha is a fortunate, prosperous, powerful, and happy man. But as is so often the case with the great monarchs of Indian legend, his happiness is flawed by his lack of a son and heir. In order to rectify this deficiency, the king resolves to perform the great Horse Sacrifice (1.8.1-2). The staging of the elaborate Horse Sacrifice, normally employed in the epics to sanctify a king's acquisition of sovereignty over his neighbors' territories, is unusual for the purpose of procuring a son. Bhatt, in his notes to the critical edition, attempts to gloss over this peculiarity by referring to the Vedic tradition, according to which "the performance of the Aśvamedha sacrifice secures everything for the performer. It is, therefore, performed even for a particular purpose (e.g. for getting a son). This explanation is far from satisfactory. For one thing, there does not appear to be any other example in the extensive list of Aśvamedhas performed in the two Sanskrit epics of a king's making such use of the rite. Moreover, as has been noted by other scholars, the king performs at least one additional rite for the acquisition of a son, the Putrīyā Iṣṭi initiated at sarga 14. One of these rites would appear to be redundant, and in the light of the seeming inappropriateness of the Horse Sacrifice in this context and of the peculiar recruitment of the sage Ṛ́śyaśṛṅga as its chief officiant, I would be inclined to disagree with Bulcke's suggestion that the superfluous rite is the one specifically designed to produce a son. It would, on the whole, appear more probable that Daśaratha's great Horse Sacrifice, which is described in far greater detail than any other ritual performance in the Rāmāyaṇa, is a later addition introduced with the purpose of firmly establishing in the mind of the audience the splendor and might of the Kosalan monarchy. By the period of the final shaping of the Sanskrit epics, the Aśvamedha had evidently become the great symbol and demonstration of Hindu hegemony. Although the Bālakāṇḍa and Uttarakāṇḍa together attribute the performance of the rite to no fewer than five Ikṣvāku kings and refer to at least eight performances of the ceremony in all, the central five books rarely, if ever, mention it. From this discrepancy, it would appear that the portions of Books One and Seven that mention this ritual, and especially the extremely detailed and elaborate account of Daśaratha's somewhat otiose performance, are late additions to the text, introduced under the influence of the Mahābhārata/Purāṇa tradition that sets such great store by the Aśvamedha.