Ezekiel was a proponent of the Babylonian approach to Temple; opposed in his life to the Levi family, the latter more Egyptian. At some point the "Zadoq" faction within Levi injected themselves as an exception to Ezekiel's rules, such that the book got readily spread around the Jews. Daniel and 11QT the Temple Scroll adopt it; New Jerusalem tries to work with it.
Despite Ezekiel's vision of the dry bones, which could support Daniel, rabbis seem to have appreciated the base text a good deal less. Tova Ganzel summarises the Rabbinic (prose) tradition. I find most-dramatic how Ganzel n. 6 raises the mishnaic ruling Megillah 4:10 against bringing his content into the haftorah. I suspect that the Babylonian Prophet rarely found much welcome in the tents of meeting.
A major issue giving to the rabbis headache was, indeed, that Ezekiel did not come from the same place as the mainline Bible had come. As mutually-aware rivals, contradictions between Bavli and Masri halakha were the whole point, of both. With both in the canon, people would have to reconcile their rivalry. The Zadokites had done this, sort of, but their attempts (like 11QT, New Jerusalem, Damascus Document et al.) went out with the Temple, any Temple.
Ezekiel's imagery proved too popular for the poets to ignore. Elʿazar's anti-Roman piyyuṭ notes the throne-chariot in all her shining glory, and Copilot tells me others bring up Ezekiel 37's dry bones. If I am reading this right, Elʿazar found a dodge around Mishnah: do it in piyyuṭ.
As to the core of how Ezekiel was nonetheless allowed to be widely read even if Jews couldn't directly utter from it at the services, this surrounds Hananiah ben Hezeqiah. He was a man of the Tannaim (up to 220 CE) who did the Mishnah. Hananiah stood forth as the one rabbi who wanted to keep Ezekiel "in circulation". The question wasn't if Ezekiel would remain canon, nor booted to join Daniel in the third-rate scribblings. Much of the tradition believes that Ezekiel owned real power - in fact, so much power it was dangerous, like Raiders of the Lost Ark dangerous. Ezekiel would instead have been locked in some secure chest like the Zohar. Christians have parallel experience with the Gnostics. Ganzel must warn that these traditions are not in Mishnah nor even Tosefta; they appear first with the Amoraim = the Talmud era, mostly complete by 540 CE. Which leads to Elʿazar's era.