Is it only possible to use the Pet Carrier, Animal Locker and Livestock Carrier on animals that are already tame? I think it would be both cool and useful if you could trap and relocate animals that are suitably vulnerable (stunned or tangled in a net, for example).
It may just be me but I find tamed animals to be really annoying to deal with. They always want to escape to follow you so you can’t just let them roam free. Wild animals, on the other hand, stay on the other side of the pen from you so you can just chase them into a corner while you collect the manure, eggs or whatever.