An idea occurred to me while pondering a mod I've been mucking about with. It might be desirable to allow for attempts to tame wildlife without cage traps first.
The first idea for this might be to make it an option in the kennels, which is presently of little use due to its prior use for training being superceded by. Being able to select which animal to bring in, from a list of those currently visible on the map, might be a useful option in the details menu. This adds to the coding complexity though.
The next step would be to go out and attempt to lure an animal. At a bare minimum it would use food in the same way it's required for taming a caged animal. The need for a rope or chain to lead it back to the kennel might be a useful flavor detail as well, or an additional balancing factor.
The advantage of this over cage traps is that it is proactive, more direct. The main disadvantage is leaving the semi-wild animal uncaged, but other disadvantages might occur as well. As with hunting, it might result in a certain level of risk depending on what animals the trainer encounters along the way.
Additionally, allowing for the animal to possibly flee or attack in response to the initial attempt to feed it might allow an additional balancing factor, and could depend on the trainer's skill level. Again, this is an optional detail that would make the idea more complex to implement, but might be useful for fleshing it out relative to the normal taming method.
Another use for this is for mods, namely ones where the playable civilization lacks access to mechanics. This brings it back to the issue of what led to this suggestion, my use of a mod for a more primitive playable civ. Being able to tame wildlife instead of relying on domestic animals would be a logical flavor detail, but doing so would require the use of mechanics.