The Mishna asks regarding a Kohen standing on another Kohen or on a vessel or upon an animal. The answer the Gemara gives relates to chatzitza and min b'mino and shel lo bimino. But the Gemara could have presented it differently, as in "You might have thought that a Kohen might be able to stand on another Kohen (who is allowed to be perform the avodah) and that might be allowed, or that a Kohen could stand on a kli sharet (since such a kli is necessary to sanctify parts of the avodah), or upon an animal (which itself can brought as a korban), but the Mishna teaches that this is not so." OR is all of that simply implicit? The way the Gemara presents the question does not address specifically why the Mishna uses the other Kohen, the vessel or the animal, as examples, as opposed to some other things.
Shalom Mark,
Thank you for your question. I understand you are asking why the Gemara frames the Havah Amina in terms of the rules of Chatzitzah, rather than the approach you suggested, that perhaps a Kohen, a Kli, or an animal would not count as a Chatzitzah because each has some connection to the Korban, whether because the Kohen is the one serving, the Kli is used for the Avodah, or the animal itself can be a Korban.
My simple take is that we do not find such a criterion in Hilchos Chatzitzah, namely that if the interposing object is thematically related to the overall Avodah then it would not be a Chatzitzah. The Gemara instead uses the standard Chatzitzah arguments, like Min b'Mino versus she'Lo b'Mino, and develops the law from those categories.
If you meant something else and I missed your point, I would be happy to clarify.
Hope this helps a bit.
Aharon Steiner