From Aitareya-Brāhmaņa:
Read this together with the Mahābhārata 👉🏾 TW
To understand why goats/Ajas are still valid pāśas for Śrautam while cows are not.
Briefly:
1. Deformed human, white deer, gayal, camel, Śarabha are ritually unfit versions of the five ideal paśus: man, horse, ox, sheep & goat.
2. The medhyatva had left the five ideal paśus in those individual instances in the primordial sacrifice performed by the Devas. It does not refer to a permanent leaving of such medhyatva for all members of the five classes as the Śruti does mention that the aja/goat remains most fit for use (prayuktatama).
3. Technically, this should mean that such Medhyatva remains in cows & horses as well. However, this has been qualified by Śișțas.
4. The Mahābhārata pramāṇa (see link above) refers to a categorical exiting of Paśutvam/Medhyatvam from cows as a class. Thus, one sees changes to a ritual such as the Śūlagava:
Original version of the rite as recorded in Āśvalāyana: TW
Modified version with gavālambhana removed as per Hiraņyakeśī: TW
5. In the case of horse, although there is no express statement (afaik) about the exiting of Medhyatvam/Yajñapaśutvam from the horse, the only rite where it is sacrificed—the Aśvamedha—is considered utsanna (gone out of use/broken down) in the Taittirīya-Samhitā itself (see last screenshot: TS 5.4.12.3) & no King in Kaliyuga has been deemed fit to perform it.
However, from time to time, some Kings did carry it out, up till even the late medieval era. However, did they let the horse run throughout the known world at that time (which would have been very vast), as it ought to have been done? The Acchavāka priest’s Saṃkṛti Sāman (song) is deemed in the Taittirīya-Śruti to make up for the incomplete Aśvamedha and complete it.