Why was it so important that the Kohen preparing the Parah Adumah be a tevul yom?

Question

Mishnah Parah 3:7 (with translation/explanation from Sefaria):

וּמְטַמְּאִים הָיוּ אֶת הַכֹּהֵן הַשּׂוֹרֵף אֶת הַפָּרָה, מִפְּנֵי הַצְּדוֹקִים, שֶׁלֹּא יִהְיוּ אוֹמְרִים, בִּמְעֹרְבֵי שֶׁמֶשׁ הָיְתָה נַעֲשֵׂית

And they would make the priest who would burn the cow ritually impure because of the Saducees, so they would not say, "it was done by one for whom the sun had set." [There are various forms of ritual impurity for which to become totally pure, one must immerse in water and then wait until the next sunset. The Saducees believed that the priest who burnt the red cow needed to be totally pure such that he'd only be allowed to do it if he waited for sunset. The sages held that he is able to burn the cow, even after only immersing in water, thus they made him impure and had him immerse so that everyone could see that they were not following the opinion of the Saducees.]

As a matter of fact, since the Kohen involved was rendered impure to a certain extent, the Sages enacted many other stringencies in the purity required for the preparation of the Parah Adumah ashes, so that people would not take it lightly. (See Rambam Hilchot Parah Adumah 2:1.)

What I'm trying to understand is why the Sages chose this hill to die on. The preparation of the Parah Adumah ashes is reported to have only happened seven or nine times in history (see Mishnah Parah 3:5). What would be so terrible if people mistakenly adopted the stricter view of the Saducees in this case? What would be the chances of a Parah Adumah naturally ever being prepared by a tevul yom (someone who has immersed and is waiting for sunset), and thus serving as a source of conflict between those following the views of the Rabbis and those following the Saducees?

Was this solely about discrediting the Saducees whenever and wherever possible, or is there something else going on?

Answer 1

I heard an explanation in the name of Rav Shimshon Pinkus ZTL, as to why the Chachamim (sages) chose the Para Adumah as one of the places to discredit the opinion of the Tzedokim.

Based on RASHI BAMIDBAR 19:22:

פרה אדמה. משל לבן שפחה שטנף פלטין של מלך אמרו תבא אמו ותקנח הצואה, כך תבא פרה ותכפר על העגל:

A RED COW — Why this rite was performed with a cow may be exemplified by a parable it may be compared to the case of a handmaid’s child that defiled the king’s palace. They said: Let the mother come and wipe up the excrement. Similarly here: since they became defiled by a calf, let its mother (a cow) come and atone for the [sin of the golden] calf. (Midrash Tanchuma, Chukat 8).

Summary: The Parah Adumah came as an atonement for the sin of the Eigel- hazahav (the golden calf).

The meforshim (commentaries) explain, (There are many sources to this, I don't have them available at present), that the sin of the B'nei Yisrael at the eigel was the request to serve Hashem through tangeble/visual "emtzaim", intermediaries.

This is rooted in the difficulty of accepting what one cannot physically see.

One of the main areas in which the Tzedokim disagreed with the mainstream Torah ideology, was regarding the acceptance of Torah-Shebaal-Peh, The oral Torah.

This is also connected to the idea of "What I see (in the written Torah with my own eyes) is what I accept.

Since the atonement of the Parah Adumah for the Sin of the eigel depended on uprooting this ideology, therefore the Chachamim felt it important to go out of their way to discredit the Tzdedokim in the process of the Parah Adumah procedure.

Answer 2

Rabbi Samson Raphael Hirsch explains in his commentary to Chukas that this command was chosen for the discrediting because it was such a public ceremony. The kohen was defiled deliberately before the ceremony's audience.