Zevachim 14b - b'rov am hadras melech

The gemara is discussing why the mishnah describes the lines of cohanim in bringing the korban Pesach.
One suggestion, to show that הולכה שלא ברגל שמה הולכה
But if we don't hold that, the gemara concludes that we need a new reason for the mishnah; it says that the mishnah teaches ברוב עם הדרת מלך.
I have a couple of questions.
1) Just like the mishnayos at the end of Sukkah by Simchas Beis Hashoeivah, the mishnayos here give a glorious description of how the Beis Hamikdash looked during these wonderful yomim tovim. The lines of cohanim here seem to be part of that: a very necessary and efficient procedure to deliver all the blood to the mizbeach fast enough.
Seems that isn't enough reason for the gemara?
2) What was the alternative anyhow, for each cohen to catch the blood [only a cohen can do kabbalah, no matter how many yisroelim can do shechitah at once], walk it all the way to the mizbeach, and do zerikah/shefichah. You'll still need every cohen you can find, working as fast as they can, running back and forth - trying not to bump into each other: they have several hundred thousand korbonos to bring in a short time.
Why isn't that ברוב עם הדרת מלך? Do many cohanim have to work on each bowl of blood to qualify? Rashi in Pesachim 64b just says שהיו כולן עסוקין בעבודה.

3) I have always assumed that the norm for korbonos was for a single cohen to do kabbalah, holachah, and zerikah. One example where we see is maseches Yoma (and Tamid) where it describes the פייס for the korbon Tamid; one cohen does all those (Yoma 25b).
We apparently don't normally prescribe lines of cohanim because of ברוב עם הדרת מלך.
Two examples that probably don't count are the avodah of the Cohen Gadol on Yom Kippur (where pretty much everything is done by the Cohen Gadol alone). Also the avodah of the Miluim in Parshas Tetzaveh and Tzav - then there was only one cohen, Moshe Rabbeinu, so of course he did everything.

On the other hand, in parshas Shemini is almost the only other detailed description in the Torah of korbonos actually brought - as opposed to commanded. And there we see four times that the b'nei Aharon הִמְצִיאוּ or הקריבו the blood or נתחים to Aharon hacohen. I haven't seen any mefarshim wonder why they were involved, instead of letting Aharon do the whole job. Some of the cases are where Aharon did the shechitah, so maybe someone else did the kabbalah - but see the mishnah in Yoma 3(4) for how the Cohen Gadol managed to do both. But that example may be the exception, as I mentioned.
Perhaps the most obvious explanation there for Yom Shemini (if we aren't going to say that ברוב עם הדרת מלך applies much more generally than I thought) was that it was a chinuch for all the cohanim, so all of them were involved as much as possible.
[Note that it says each time that it was done by בני אהרן - not by just one of them.]

I was able to ask R' Zvi Berkowitz shlit"a this question. He answered that ברוב עם הדרת מלך is applicable when a lot of people do a mitzvah together. It may not be enough for all of them to be together doing mitzvos, if they are doing separate mitzvos.
He gave as a possible example, nine people who want to daven together without a minyan. It may be a beautiful thing, but without a minyan to combine them there may not be an inyan of ברוב עם.
He certainly did not think that this was something to do on every korbon. It was just how Chazal were able to identify an advantage of having many cohanim work on each korbon as in the mishnah, as opposed to the alternative procedure of having lots of cohanim, each one doing everything for each single korbon, over and over. Both procedures involve all the cohanim, but only the first has the ma'aleh of ברוב עם.