1)
Why did Moshe receive the chest of the Eil ha'Milu'im?
1.
Moshav Zekenim: Because Hashem does not deny anyone's reward. 1
2.
Zevachim, 101b: Because (for the seven days of Milu'im) he was a Kohen Gadol who received a portion in Kodshei Shamayim. 2
1
And if Moshe wwho served once as a Kohen received a share in the Kehunah, how much more so Aharon, who is the Kohen Gadol permanently! As the Navi writes in Mal'achi 1:10 "Mi? Veyisgor Delasayim ve'Lo Sa'iru Mizb'chi Chinam".