As long as the animal is also happy and cared for, then utilizing a relationship with a pet to cultivate empathy is a healthy, normal, pro-social behavior which makes the world a better place. You could say it's a symbiotic relationship of wise exploitation.
(EDIT: To clarify, the difference here is that challenges which arise in such relationships serve to grow and enhance empathy and love. Whereas with a work animal / tool, challenges in the relationship means discarding the beast and replacing it with something more useful)
As far as the hypothetical situations go, it's a red herring that I don't have the time to dive into.
"As long as the animal is also happy and cared for, then utilizing a relationship with a pet to cultivate empathy is a healthy, normal, pro-social behavior which makes the world a better place." emphasis mine
This is a highly speculative opinion that provides no cost benefit analysis.
Everything is a resource regardless of whether it is exploited. The person saying empathy comes from having exposure to pets is in essence saying pets are a resource to cultivate empathy and should be exploited as such. The issue is resource constraints. Pets consume a lot of argicultural and pharmaceutical resources.
You talk of love and empathy being unconditional, but when you live in a resource constrained world, should we spend money creating, housing, and feeding pets? Or should we care for the vulnerable humans? Should we stop keeping pets so that we don't need the agriculture that is required to support them, thus feeding people or allowing the land to return to the natural world and it's native animals?
Resources are a part of the equation. It seems many people ignore the n-order impacts. It's the same as people buying their processed food or meat without ever seeing the source and process. Probably even more so with kibble since it doesn't look like food to us.