Not at all clear that the Torah disagrees. Just because the Torah permitted it, does not mean that one who abstains because of Tzaar Baalei Chaim is not a big Baal Madreiga. There is some halacha regarding the lung of an animal that was collapsed in a certain way, because the animal was in great fear, such as if its fellow animal was shechted in its presence. So clearly animals do not enjoy the shechita process. Why the Torah permitted it may be like the Yefas Toar.
We are also permitted to be gluttons and eat all day. Nevertheless, the higher madreiga is to eat only enough to be healthy.
The Torah also permits a man to withhold a get for huge sums of money.
So just because the Torah permits something does not mean it is giving its endorsement.
Again, the highest madreiga is menschlachkeit.