This is an interesting question and my response is two-fold:
1) From a practical standpoint, in terms of the blood and gore, it couldn't
be any worse than what happens to the animals whose meat we eat as hot dogs
or hamburgers everyday without thinking about it. The only differnce is
that it is done in a slaughterhouse so that we don't have to see it. Also,
not only did the priests and others eat the sacrifices for their food, but
also, the Israelites, I believe, ate very little meat outside of the those
slaughtered in the Beit HaMikdash, certainly much less than we consume
today. Many more animals suffer and die today in slaughterhouses, and for a
lesser purpose than in the Beit-Hamikdash.
2) Secondly, from a spiritual standpoint, perhaps the most fundamental
precept of Torah is that there is no expiation from sin without the shedding
of blood. It is written in Lev. 17:11, "For the nefesh (life) of all flesh
is in the blood, and I have given it to you upon the altar to make atonement
for YOUR nefesh (l'chaper nafshechem)." Strange as it may seem, through the
life of an innocent being, our sin is covered, and the punishment that we
deserved is placed upon them in our place. As horrible as it is, it is
necessary according to G-d's system for the sinner to lay hands on the
animal, and then see and witness the blood of the innocent being that is
taken up in his place. This witness is absolutely necessary in order to
help the sinner to truly repent and receive the forgiveness that Hashem has
promised.
Without the repentant heart, it is true that the sacrifice is none
other than a drop in the "coin box", and, in fact, the words of our Prophets
declare that the lack of repentance on the part of Israel is exactly the
reason that G-d took the Beit HaMikdash away from us two times already,
challenging us to serve him in truth, before it shall be rebuilt.
Michael Stepakoff