We (and the kohanim) are to eat the kobanot satiated (see below for sources). What is the reason behind this mitzva? It would seem that we would get more enjoyment from eating if we were hungry.
Was the korban pesach eaten only when satiated? quotes the Rambam giving this halacha about Korban Pesach only, but the Rambam does not say why it is so.
Update: Regarding other korbanot, I offer this "all sacrifices must be eaten when one is satiated, to make sure that one does not leave the table of the King when hungry, thus giving a sense of honor and respect to the eating of the sacrifice." Source: http://www.yutorah.org/lectures/lecture.cfm/743728/harav-avigdor-nebenzahl/the-korban-todah-and-sippur-yetziat-mitzrayim/
I see this reason as a non-sequitur rather than a logical reason. If I am invited to go to Shabbos lunch on a day that my shul has a great kiddush, I try hard not to eat anything at the kiddush so I have a good appetite for the lunch. I would think a kihg's table would deserve, even demand, a good appetite as well.