Or, as Michael wrote in a comment on a previous post:so that the bread was obviously warm (and fresh) on the day they took it away from its place. If so, perhaps this question is without foundation. As an alternative, perhaps the purpose of the show-bread, and its very avodah, was to sit there for the week, looking pretty. At the end, of course the kohanim could eat it, but that was not the purpose. And when it was put up, it was fresh.
But what about in the general case. When we say:
what is wrong with these maimings? Is Hashem a picky eater? Of course not! As we see in Navi, Hashem does not really hunger for our sacrifices. Furthermore, don't we say that rachmana liba ba'iy? Rather, if I may may a derasha on leratzon in pasuk 20, much as Ibn Ezra does about the day of the omer, I would say: The korban has to be an offering given with full heart.
While Hashem does not care whether the korban is X or Y, but people do. It is the thought that counts, but what in the world was he thinking? Since culturally people consider this non-optimal, is the person giving his refuse to the altar? This bull is no good for breeding, so if I am going to offer a korban, I might as well give this deficient one.
The same for a kohen, perhaps. We even see in sefer Shmuel that people can donate children to work in the mishkan:
Even among kohanim, was it necessarily so that every one went into the service, from each family? It is possible that they may choose. Well, this person cannot be an accountant, because he has no head for numbers, so he might as well be a kohen. He is maimed anyway; let him be set for life with food, and have a steady job. There is, perhaps, some choice on the part of the people who serves. If so, this also reflects the spirit of the people and their attitude towards Hashem.
As another possibility, like the Minchas Chinuch, of course Hashem does not care, but the purpose of the Mishkan/Beis HaMikdash is to present a certain presentation to the people, to help them relate to God. And people do care about these things, and are bound by their cultural attitudes. And back then, and indeed until fairly recently, seeing maimed animals or maimed people as part of the service would have lessened the experience in their eyes, where the purpose is to draw people closer to Hashem.
Those are two possible answers. There may of course be more, and one might even be correct. :)