It is somewhat unclear from the sugyos what exactly the function of prisha is. At first glance it would seem to be for the purpose of tahara, but this cannot be. The gemara 6a asks, that although Rav Yochanan learns from miluim and Reish Lakish from Sinai that there needs to be prisha, why do we need to separate him from his wife. The gemara responds that there is an additional concern of tu'mah (which the gemara explains on 4a that Reish Lakish requires 7 days, as opposed to the 6 day prisha of Sinai). Clearly, the gemara holds that there is a purpose of prisha that is learned from miluim or sinai, even if we would not maintain chumros of tahara. Another option of what prisha accomplishes is to keep people away from him to avoid tu'mas meis. However, the gemara 6b debunks this possibility as well because the gemara (as explained by rashi) takes for granted that he is allowed to have visitors and we are not concerned that they will drop dead while visiting him. The braisa 4a also describes that there are kohanim working with him all 7 days to teach him how to do the avoda. We are still left with the question, what is the definition of prisha?
The gemara cites a braisa contrasting the prisha of the kohein on Y.K. and the prisha for the parah aduma. The braisa says - שזה פרישתו לקדושה ואחיו הכהנים נוגעין בו, וזה פרישתו לטהרה ואין אחיו הכהנים נוגעין בו. The braisa holds that the function of prisha for parah aduma was clearly a tahara issue, but for Y.K. was not primarily a tahara issue, it was for the purpose of "kedusah". What does this mean? Rashi writes that it is a preparation for entry to the machaneh shechina by separating him to not be arrogant and not be frivolous, in other words, putting him in a serious state of mind. It seems that according to Rashi the function of the prisha is a mental preparation for the avodas hayom.
Tosafos on 2a (d.h. mai shena) writes explicitly that the definition of פרישתו לקדושה means that since he was going to be doing avoda in the kodesh hakadashim, they would separate him into a chamber that was built b'kodesh. Although Tosafos 6a (d.h. m'beiso) writes that the lishkas parhedrin was built b'kodesh (machaneh shechina - azara) but open into the chol (machaneh leviya - ezras nashim), so that it would not have kedusah of azara (to enable him to sit and sleep there). Why is this considered פרישתו לקדושה since the place didn't actually have kedusha status? Tosafos 8b offers two approaches. The first approach is that since it was built in the azara which had kedusha of machaneh shechina, it was considered פרישתו לקדושה even though the actual chamber didn't have kedusha. A second approach is the opposite, it was built in chol and open to kodesh so the inside had kedusha for the purpose of eating kodshei kodshim. Nevertheless, since it was built b'chol not b'kodesh, it didn't have full kedusha of the azara so he was able to sit and sleep there. Tosafos at the end rejects the second approach and holds that if it is open to kodesh, sitting would not be allowed.
Tosafos clearly holds that the function of prisha for the kohen gadol before Y.K. is to place him in a kadosh place as preparation for avoda לפני ולפנים. The difficulty with this approach is that Tosafos explains the question of the gemara on 6a - מביתו למה פירש to mean that although we need to separate him, why should we put him in the lishkas parhedrin where he can't be with his wife, we should put him in one of the mechilos that didn't have kedusha where he can be with his wife? The gemara answers that there is an additional concern of tu'mah. The question of the gemara implies that the function of prisha cannot be to put him in a place of kedusha, because if that were the case, it wouldn't makes sense for the gemara to suggest that instead we should put him in one of the mechilos that didn't have kedusha?