Song of the Day as Second Temple Practice but Not Talmudic Practice

I recently came across this interesting excerpt dealing with the song of the day as practiced in the Second Temple:

...the daily Levitical songs (Pss 24, 48, 82, 94, 81, 93, 92) as recorded in a baraita appended to the end of m. Tam. as evidence.³¹ According to this baraita, the Levites would sing these psalms during the burning of the daily sacrifice. This passage provides proof for a rabbinic memory of a Second Temple practice, nothing more. There is no evidence that these psalms were part of daily rabbinic liturgy until well after the talmudic period (ca. 650). No talmudic discussion regards the recitation of these psalms as anything other than temple practice.³² Contrast this with other prayers that are initially imagined as part of temple ritual and are discussed elsewhere in terms of contemporary rabbinic liturgy, such as “True and Firm” (emet veyatziv) (m. Tam. 5:1; t. Ber. 3:6). The most compelling evidence for their absence in early rabbinic liturgy is the fact that even in the Geonic period these psalms appear to be non-liturgical.³³ Seder Rav Amram Gaon strangely claims that one recites the baraita about these psalms and not the psalms themselves,³⁴ and the prayer book of R. Saʿadyah contains no mention of them. The earliest positive evidence comes from Maimonides’s prayer book, found at the end of his Book of Love, which claims: “And a small part of the nation has a custom to read after all of these supplications the psalm that the Levites would sing in the temple on that day” (section 34).³⁵ Even in the time of Maimonides, the daily recitation of these psalms was nothing more than a practice of the few.³⁶ The early rabbis clearly did not adopt the Song of the Levites into daily liturgy.³⁷

-Abraham Jacob Berkovitz, "The Life of Psalms in Late Antiquity" (PhD diss., Princeton University, 2018), 165-166. 

And for those interested in the relevant footnotes, enjoy: 

31. On this appended baraita, see Epstein, Introduction to the Text of the Mishnah, 2:979.

32. Rabbinic sources lavish much attention on the use of these psalms in temple ritual. In what is no doubt an innovation, the rabbis argue that the daily psalm is an integral part of temple liturgy and that anything which can jeopardize its proper recitation must be fixed. M. Rosh Hash. 4:4 begins with: “Originally, they would accept testimony regarding the New Moon all day, but once the witnesses delayed in coming and the Levites said the wrong psalm.” The Levites had accidentally sung the song of the day instead of that of the New Moon. On proper psalmody as an essential aspect of sacrifice, see also y. Ta'an 2:2 67d, “Priests, Levites, Israelites and psalms can invalidate a sacrifice.” I plan on exploring this and other passages in a future study about Psalms in rabbinic memory. 

33. Robert Brody, “Liturgical Use of the Book of Psalms in the Geonic Period,” in Prayers That Cite Scripture, ed. James L. Kugel (Cambridge: Harvard University Press, 2006), 75; Israel Ta Shma, “Sources and Place of the Prayer ‘It Is Upon Us to Praise’ in the Prayer Book,” in Book of Remembrance for Ephraim Talmadge, ed. Dov Lipschits (Haifa: Haifa University Press, 1993), 93–94. 

34. Daniel Goldschmidt, ed., Seder Rav Amram Gaon (Jerusalem: Mossad HaRav Kook, 1971), 40. 

35. On this, I follow Brody, “Liturgical Use,” 57, n. 59 that the mention of this custom in Sof. is a later addition. 

36. Who are these “few”? Is this a way Maimonides signals a common Palestinian custom? 

37. Fleischer, Prayer and Prayer Customs, 163 claims to find no mention or use of these daily Levitical psalms in any of the Genizah fragments he works with.