An interesting tangent is that this could entail the extinction of several human-designed strains of animal which are not well equipped to live in the wild.
So mote it be I guess.
Base genetics are still around for the chicken, pig, and sheep, but the Aurochs's extinction means we irrevocably altered the cow. I'm sure a few varieties of cow would adapt to the wild though.
Buffalo may need to keep their vestigial wings too.
More broadly, the answer is that it doesn't really matter that much. Species go extinct all the time, and with humans around the rate has been astronomically higher. Replacing animal products with plant based or cell based products might even have a net benefit in extinctions, since land that would otherwise go towards feeding and raising livestock could instead be let back to nature.