If you could walk up to deer and popthem in the head with a gun or captive bolt, then shooting them with a bow would be hardly justified. Same goes for a tame cow.

Instant massive brain trauma will not be felt. The same cannot be said for an arrow through the chest. Using the word 'suffer' may be subjective, but the point is, why prolonge the cow's death by even a few seconds to satisfy a personal curiosity?