Why is the Parah Adumah Here?

OK, it's open mike time.

Parshas Chukas is perhaps most well-known for its opening section, which includes the laws of the parah adumah and tum'as mais. Why are these halachos inserted at this point, though? The question is amplified by the fact that parah adumah is known to be one of the three (four?) halachos that were taught at Marah before Matan Torah.

Rashi (20:1), citing Mo'ed Katan 28a, notes that Parah Adumah is juxtaposed to the subsequent death of Miriam to teach that just like the parah adumah is mechaper[1], so, too, is the death of tzaddikim.

The previous Rashi expounds on the passuk's use of the term "kol ha-eidah" to learn out that all of those who were condemned to die in the midbar had already died at this point, leaving only those who were designated to enter the land. Hence, perhaps the inclusion of a halachic parsha about death and purification serves as the Torah's summary of the thirty-seven years between the rebellion of Korach and the death of Miriam, which were entirely devoted to the deaths of the failed dor ha-midbar and nothing else (as indicated by HaShem's silence towards Moshe during these years).

Any other suggestions?

[1] Tosefos there quotes one of the numerous ma'amrei Chazal which indicate that the Parah Adumah was mechaper for the sin of the eigel, although it's interesting that the Yoma 2a specifically rejects the idea that the Parah Adumah is for kaparah, instead spending the next daf-and-a-half suggesting a whole litany of korbanos that
could instead be exegetically alluded to by the use of the word "l'chapeir" in a passuk, before finally settling upon the avodah of Yom Kippur. A variant text of Rashi compares the death of tzaddikim to korbanos, but as the Parah Adumah was not a korban, the basis for this comparison is difficult to me.