Let's dwell a bit more on Leviticus 16. In note 41 on page 230 of Cult and Character, Gane writes: “In this verse [Lev. 16:33] כפר את takes the three parts of the sanctuary as direct objects because the blood is physically applied to them, but purification of the people is expressed with כפר על. Although these sacrifices benefit the people, the preposition על acknowledges that this benefit is not direct in the same way." This statement is a perfect example of how a grammatical point can be overinterpreted for doctrinal gain. כפר על is frequently used with inanimate objects to which blood is applied (even in Lev. 16). And isn't Gane relying on the same prepositional usage of the verb to argue for his theory of exclusive purgation of the sacrifice offerer(s) in Leviticus 4 and 5? Why wouldn't על indicate indirect benefit in the case of outer-sanctum and outer-altar offerings too?
Following many commentators before him, Gane also assumes that the high priest's bathing of Lev. 16:24 is a final step in the removal of sin and impurity from the sancta (and the priesthood). This interpretation fails to notice that the high priest also bathed before entering the sanctuary (v. 4). These priestly washings had nothing to do with shedding guilt or impurity collected from the sanctuary, but were part of the preliminary ritual that also included donning vestments (see m. Yoma in the Mishnah). Ex. 30:20-21 clearly states the apotropaic purpose of temple washings (similar to that of incense use in Lev. 16:12-13), and distinguishes between two types of cultic activities that are preceded by washings - entering the sanctuary and approaching the altar to sacrifice (a distinction obviously mirrored in the duties of the high priest on Yom Kippurim). Thus, there is no hint of decontamination in Lev. 16:24.
Even more remarkably, there is no mention of contamination in verses 26 and 28 either. Contrary to another popular assumption, the persons charged with the disposal of animals do not become unclean. Their ritual use of water is simply a rite of passage (the Mishnah is helpful here too, even if it does use the language of impurity, citing the legal opinion that impurity is incurred by exiting the city, not by contact with supposedly contaminated animals). This meaning of the mikveh is attested in passages such as Lev. 13:6, where the transition from a liminal state (quarantine) to regular community integration is done through water. Being quarantined did not equal being impure (cf. Lev. 13:11). But the road back to community passed through water (this context also illuminates the fact that establishing purity is not necessarily the reversal of a previous condition of impurity - see also vv. 58-59). Additionally, we know from Lev. 4:12 that the carcass of animals whose blood was brought into the sanctuary was to be burned in a clean place outside the camp. Thus, there is no hint of decontamination in Lev. 16:26.28.