(Underline mine) I need to clarify some thing here. It was a time when the Aryan/Indigenous assimilation had taken place. The indigenous shamans had been included in the Aryan fold as Brahmins (perhaps Shakyas and Lichhavis also were indigenous chieftains who had been assimilated as 'kshatriyas'). That is not saying that some Vedic brahmins may have advocated animal sacrifices but the indigenous shaman/brahmins too might have been involved.
Agreed, it was not only Brahmins who encouraged merit via sacrifice, nor can it be assumed that all Brahmins encouraged sacrifice as a means to get merit.
Here are some sutta snippets to help get an idea as to why Buddha made the 3-fold rule:
Then the brahman Sangarava went to the Blessed One and, on arrival, exchanged courteous greetings with him. After an exchange of friendly greetings & courtesies, he sat to one side. As he was sitting there he said to the Blessed One: "I say, Master Gotama. We brahmans perform sacrifices and get others to perform sacrifices. And whoever performs a sacrifice, whoever gets others to perform a sacrifice, they have all practiced a practice of merit — the business of a sacrifice — [that benefits] countless beings. But whoever, leaving his family, has gone forth from the home life into homelessness, and tames his single self, brings his single self into tune, brings his single self to Unbinding: his practice of merit — this business of going forth — is one [that benefits] only one being."
"Very well then, brahman, in that case I will cross-question you. Answer as you see fit. What do you think? There is the case where a Tathagata appears in the world, a worthy one, rightly-self-awakened, consummate in clear-knowing & conduct, one who has gone the good way, knower of the cosmos, unexcelled trainer of those who can be taught, teacher of human & divine beings, awakened, blessed. He says: 'Here! This is the path, this is the practice that, having practiced, I make known the unexcelled coming ashore in the holy life,
[1] having directly known & realized it for myself. Come! You, too, practice in such a way that you will remain in the unexcelled coming ashore in the holy life, having directly known & realized it for yourselves.' Thus the Teacher teaches the Dhamma, and others practice, for Suchness. And there are countless hundreds of them, countless thousands of them, countless hundreds of thousands of them. This being the case, is this practice of merit — this business of going-forth — one that benefits countless beings, or only one being?"
"This being the case, Master Gotama, this practice of merit — this business of going-forth — is one that benefits countless beings."
When this was said, Ven. Ananda said to the brahman Sangarava, "Of these two practices, brahman, which appeals to you as the less complicated, the less violent, the more fruitful, & the more rewarding?"
When this was said, the brahman Sangarava said to Ven. Ananda, "Just as with Master Gotama & Master Ananda, I worship them, I praise them [both]."
A second time, Ven. Ananda said to him, "I didn't ask you whom you worship and whom you praise. I ask you, 'Of these two practices, brahman, which appeals to you as the less complicated, the less violent, the more fruitful, & the more rewarding?'"
A second time, the brahman Sangarava said to Ven. Ananda, "Just as with Master Gotama & Master Ananda, I worship them, I praise them [both]."
A third time, Ven. Ananda said to him, "I didn't ask you whom you worship and whom you praise. I ask you, 'Of these two practices, brahman, which appeals to you as the less complicated, the less violent, the more fruitful, & the more rewarding?'"
A third time, the brahman Sangarava said to Ven. Ananda, "Just as with Master Gotama & Master Ananda, I worship them, I praise them [both]."
Then the thought occurred to the Blessed One, "Being asked a legitimate question by Ananda up to the third time, the brahman Sangarava evades it and does not reply to it. Suppose I were to get him out [of this dilemma]."
So the Blessed One said to the brahman Sangarava, "Brahman, what was the topic of conversation that arose today when the royal court sat gathered in the royal palace?" (continued at this
link.)
This sutta shows that sacrifice was not encouraged among all Brahmins:
A. "There are some contemplatives & brahmans who hold this doctrine, hold this view: 'There is nothing given, nothing offered, nothing sacrificed. There is no fruit or result of good or bad actions. There is no this world, no next world, no mother, no father, no spontaneously reborn beings; no brahmans or contemplatives who, faring rightly and practicing rightly, proclaim this world and the next after having directly known and realized it for themselves.'
[1]
B. "Some contemplatives & brahmans, speaking in direct opposition to those contemplatives & brahmans, say this: 'There is what is given, what is offered, what is sacrificed. There are fruits & results of good & bad actions. There is this world & the next world. There is mother & father. There are spontaneously reborn beings; there are contemplatives & brahmans who, faring rightly & practicing rightly, proclaim this world & the next after having directly known & realized it for themselves.'
"What do you think, householders? Don't these contemplatives & brahmans speak in direct opposition to each other?"
"Yes, lord." (more at
this link)
This sutta shows that sacrifice was not limited to Brahmins, and what is more enlightened than sacrifice:
This was said by the Blessed One, said by the Arahant, so I have heard: "All the grounds for making merit leading to spontaneously arising (in heaven) do not equal one-sixteenth of the awareness-release through good will. Good will — surpassing them — shines, blazes, & dazzles.
"Just as the radiance of all the stars does not equal one-sixteenth of the radiance of the moon, as the moon — surpassing them — shines, blazes, & dazzles, even so, all the grounds for making merit leading to spontaneously arising in heaven do not equal one-sixteenth of the awareness-release through good will. Good will — surpassing them — shines, blazes, & dazzles.
"Just as in the last month of the rains, in autumn, when the sky is clear & cloudless, the sun, on ascending the sky, overpowers the space immersed in darkness, shines, blazes, & dazzles, even so, all the grounds for making merit leading to spontaneously arising in heaven do not equal one-sixteenth of the awareness-release through good will. Good will — surpassing them — shines, blazes, & dazzles.
"Just as in the pre-dawn darkness the morning star shines, blazes, & dazzles, even so, all the grounds for making merit leading to spontaneously arising in heaven do not equal one-sixteenth of the awareness-release through good will. Good will — surpassing them — shines, blazes, & dazzles."
When one develops — mindful — good will without limit, fetters are worn through, on seeing the ending of acquisitions. If with uncorrupted mind you feel good will for even one being, you become skilled from that. But a Noble One produces a mind of sympathy for all beings, an abundance of merit. Kingly seers, who conquered the earth swarming with beings, went about making sacrifices: the horse sacrifice, human sacrifice, water rites, soma rites, & the "Unobstructed," but these don't equal one sixteenth of a well-developed mind of good will — as all the constellations don't, one sixteenth of the radiance of the moon. One who neither kills nor gets others to kill, neither conquers, nor gets others to conquer, with good will for all beings, has no hostility with anyone at all.
-source-
I hope this clears up any misunderstanding.