Pets are expensive.

But, They say they are hard to code. You have mounts, and pets. What about a third choice?

Say I want one of those sheep I keep running into. I take it off somewhere, feed it, give it shiny things. Now, in real life, the pet would likely hang around.

Perhaps have some kind of artifact that you can use on non-sentient mobs? Would be nice to have a cockatrice or something. I swear, it isn't that hard for You! It would be darn near the same to the mounts artifact.

Maybe if they don't hang around for long. Like, if they waddle off on their own accord if they lose interest, or they notice no more food is coming their way.