I forget which city but somewhere in Greece the defenders dissuaded war elephants by dangling a lively (and very pissed off) pig from the top of an outer wall. Actually coating their backs with pitch and lighting them ablaze and releasing them may not have been done like people think. What if that pig turns and runs through your own ranks instead? Pigs succumb to arrows the way most things do too it should be noted.
Traveling during wartime with pigs is probably not easy. People will want to eat them. They overheat and aren't pack animals either, so you transporting them by cart? Sure would be a choice gig though, being the war pig handler. Let everyone else tangle with those Goths and Celts while you secure the rear, protect that delicious Legionnaire Chris P. Bacon.
Romans found out elephants panic at the smell of horse blood, so killing an animal that's already a component of war and travel? Way easier. And being Italian, they'll eat it anyway.