Is "baby daddy" trashy?

Good Lord almighty have I heard "my baby daddy" this " her baby daddy" that. All I can think of is how unintelligent that sounds. It doesn't even make sense. Its like saying "my cat tail" when you're referring to your pet felines attached elongated sacral bones not the purple fuzzy tail keychain y'all hang off your pant loops. "My baby's daddy" would make sense. "My baby's father" would be way more respectful. I get sometimes it's SPECIFICALLY TO disrespect the maybe not so great father but please ladies can we all look out for each other and help each other sound a lil more educated? ✌