After helping Auntie Han with her birth, and witnessed the heartbreaking death of some of the cubs, she could have been traumatized from ever wanting to have cubs herself. But for some reason, she was not. That was just life, and it was the reason you didn't name the cubs until you were reasonably sure they'd survive. Her mother Buna must have had her doubts about her at some point since she was named 'this one will not die'...
Kokumo felt ready to raise her own daughters, and by now Bangizwe was 'tried and true' so to speak. He sired strong cubs, she knew that. Hopefully he'd agree to her proposal... but she was Enkulu now, that would count for something, right?
Quaji