Our Rav was discussing kisui hadam (the mitzva of covering the blood after slaughtering), and referenced Rav Kook as suggesting this mitzvah shows that the Torah would prefer that we didn't eat meat. But how does he deal with the fact the mitzvah excludes domesticated animals?

Rav Kook explicitly explains there in that very paragraph, that if one of the benefits of covering the blood is to heighten our morality (we cover things that should bring embarrassment), the question is how to achieve that goal. Regarding domesticated animals slaughtered in the city and close to home, the goal of repulsion is achieved by not (!) covering the blood and getting "grossed out" upon seeing blood which disturbs our hygienic surroundings. On the other hand, the mitzva is to davka cover blood when slaughtering wild animals and birds (most of which are not domesticated) out in the wild, where everything is gross (remember the "scuzzy" feeling on the 3 day "Machaneh Shmutz" in Moshava without running water...), so we're not repulsed so much by some more blood- but then the desired effect is davka achieved by covering the blood, reminding that we should be embarrassed by our present level of that immoral desire to kill and eat animals. For more on the topic, see https://www.yutorah.org/lectures/1054685/ Rav Ari Shvat (Chwat)