Q. The Mishna says that the Kohen Gadol was made to stay awake leil Yom Kippur and was prevented from sleeping, lest he come to have an emission and become disqualified from doing the avoda.
But what is the problem – wasn’t there a substitute Kohen who was prepared to replace him, as it says in the very first Mishna in the tractate? So what is the big deal if the Kohen Gadol would become impure?

A. Most likely the replacement wasn’t as great or outstanding as the original Cohen Gadol, otherwise he would have been the one chosen to perform the avodah. The Mishna in Pirkei Avos (5: 7) quotes as one of the ten miracles occurring in the Bais Hamikdosh, the fact that a Cohen Gadol never became disqualified by having a seminal discharge on Yom Kippur. Mefarshim (Bartenura ibid., Ritva, Tosafos Yom Tov Yuma 21a et. al.) explain that although other mishaps and acts of unfitness did occur, this type of rejection was seen as a major embarrassment and an overwhelming shame, not only to him but also to the people he represented. Meforshim make a point that during the second Bais Hamikdosh, the Cohanim Gedolim were not necessarily the greatest tzadikim.
See Talmud (Yuma 88a) regarding present-day.

Rabbi A. Bartfeld as revised by Horav Shlomo Miller Shlit’a