Is taming of wild animals strictly a manipulation, or is it divinely assisted to soften their instincts to help preserve them if they would otherwise be destroyed?

This is a good insight because it is quite true. This is the influence we can bring to bear and is used again and again with interlopers to soften them, at least for a time, to help sidestep an encounter with a human reaching out in prayer for help, so their life can be preserved or a more dire circumstance of torment prevented from taking place. This can have a carryover effect and serve to begin to soften things and render them more healable. In the case of animals, this can help preserve their life as you reflected in your question. Many animals captured from the wild are allowed to live a much longer time when they can tolerate humans in their presence or even have a kind of relationship as an exotic pet, and this is a win-win for the human handler as well as the animal. While some would say it robs them of the dignity of their wild nature being truly who they are, we would point out that the innate savagery of the wild beast serves them in a savage, competitive environment, but does not serve them any longer when they are in a constrained environment where savagery is not necessary for survival, but only represents a threat to other life and ultimately their own if it might lead to them being destroyed.