When my wife calls me 'dad' or 'daddy' I know she might be talking as well to one of our kids instead of to me. It gives it context, and it also does something with me by increasing my responsibility instead of slacking. After all, if you are once a dad or mom, you're always one.

Honestly, I think its a great way to get some perspective (but I am on the spectrum). I also find it plain fun, and -sometimes- cute. Doesn't mean I always do it in family circle. Its just that, in a work environment, there's an etiquette, and this one isn't part of it. If you're too different (e.g. weird in this context), they don't want you, and one way or another you'll get cast out. Goes for weird people too.

Counterexample - When my wife calls me daddy she’s definitely not referring to my role as a father.

Are you sure she is not subtly convincing you to take the role? Presumably she is temping you into the manner in which it happens.

A perfect example of the importance of context.

You are not just ”a person” when you are a parent. You are a person with a very special role and you spend a lot of time acting in that role. As I see it, the border is fuzzy and the overlap large, but the role and the person are not the same.