It's clear to me why he had to carry out the special Avodah of the day described in Parashat Acharei Mot.
But why did he have to do everything else, such as the Tamid and the "ordinary" Musaf similar to that offered on other festival days?
We find that significant changes were made to the Kelim used on Yom Kippur to make things easier for the Kohen Gadol. Why not make it really easy by not requiring him to do all of the ordinary daily and festival Avodah?
The question is dealt with in this article at yeshiva.org.il which it is better to read.
My summary: he quotes:
Ritv”o – If the KG is unable to do the avodos which are not specific to Yom Kippur, they can be done b'dieved by another Kohen.
Baal Hameor – KG has to do everything including removing the ashes (תרומת הדשן).
Ramban in Milchamos – The lotteries (פייסות) mentioned in the mishna in Yoma are applicable to Yom Kippur, KG does not remove the ashes.
Mikdash Dovid – KG has to do one of the avodos of the korban tomid but not all.
So the KG does not have to do everything else, such as the Tamid.
