Cats are social animals, they can get bored and/or sad if they are alone for long periods. HOWEVER I don't know how common that is. I've had cats all my life and usually they have hated each other. I currently have 2 sets of siblings (4 cats) and they all hate each other in some way or another and are almost always in different rooms from each other. Just my 2 cents whenever I see this come up. I've known many many happy single cat households.
That's a really good point about cats not getting along. I would be disheartened if I adopt another kitten with her and they grow to dislike one another. Thank you.