In Yoma 37a and Zebhahim 20a we learn that:
בן קטין עשה שנים עשר דד לכיור אף הוא עשה מוכני לכיור שלא יהיו מימיו נפסלין בלינה
Ben-Qattin made twelve spouts for the laver; he also made wheels [pulleys] for the laver, so that its water should not become unfit through the passing of the night.
The Rambam writes (H. Beth ha-Behirah 3:18):
הכיור--היו לו שנים עשר דד, כדי שיהיו כל הכוהנים העוסקים בתמיד מקדשים ממנו כאחד. ומוכני עשו לו, שיהיו בה המים תמיד; והיא חול, כדי שלא יהיו המים שבה נפסלין בלינה: שהכיור מכלי הקודש, ומקדש; וכל דבר שיתקדש בכלי קודש--אם לן, נפסל.
The washbasin had twelve taps, so that all the priests who were involved in offering the daily sacrifice could sanctify [their hands and feet] at one time. A mechanism was made so that it could be filled with water at all times. [The mechanism itself] was not sacred, and thus, the water remaining in it did not become invalidated [for future use] because the night passed. [This was necessary] because the washbasin was a sacred vessel and sanctified [its contents]. Anything which is sanctified by a sacred vessel becomes invalidated [for future use] after the night passes.
The Bartenura (Yoma 3:10) notes:
שנים עשר דד לכיור: כדי שיהיו שנים עשר כהנים הזוכים כפייש של תמיד השחר מקדשים בבא אחת ואע"פ ששלשה עשר כהנים היו כדאמרן כפרקא כראשונה לא עשה דד לשוחט שהשחיטה כשרה בזר
Twelve spigots for the Kiyor: In order so that the twelve Kohanim that merited in the lottery to participate in the Tamid ha-Shahar could sanctify themselves all at once, even though there were thirteen Kohanim as explained in the first chapter another spigot was not made since the slaughter is acceptable even when performed by a non-Kohen.
So it seems that even though thirteen Kohanim regularly participated in the daily routine, only twelve actually would have needed to wash their hands and feet. So far, so good... twelve makes (sufficient) sense. However we also learn that there were occasions on which a greater number than thirteen Kohanim participated. The Gemara in Yoma 26b teaches:
תני רבי חייא: פייס פעמים שלשה עשר, פעמים ארבעה עשר, פעמים חמשה עשר פעמים ששה עשר
R. Ḥiyya taught: Sometimes the lottery [for selecting Kohanim for the different abhodoth] was for thirteen, sometimes for fourteen, sometimes for fifteen, sometimes for sixteen.
So there were definitely occasions on which more than twelve/thirteen Kohanim would have been chosen to participate (see Rashi ad loc on the different occasions that would give rise to necessitating the abhodah (service) of additional Kohanim).
Given that there were times of the year that more than twelve Kohanim would have been selected to perform the various abhodoth, why did ben-Qattin redesign the the Kiyor to only have twelve spigots? If there is some advantage to having the Kohanim all wash at once, why weren't there more spouts?
Some ideas that occurred to me are: A) maneuvering the Kiyor was kind of a big deal, so much so that the mechanism for raising/lowering it every day was said to be heard from Jericho (Tamid 3:8), maybe keeping it just to twelve alleviated the burden - but then I pushed that thought away with "this is the Miqdash, go big or go home! what's a few more spigots?" B) Perhaps any bigger and it would have interfered with the operational space, possibly infringing on the routes the Kohanim would have taken to perform their designated tasks C) Perhaps the additional abhodoth on the days with expanded abhodah didn't require washing?
Are there any sources that discuss this? Am I overlooking something basic?
