My cat that I have now isn't at all like that. She's a wild child.
The cat that I had growing up was somewhat like that and was very chill when I had my migraines and when I was home sick from school would lay at my feet.
Now, I did have a cat from the time I was about seventeen until I went through my divorce (she went with her "dad") and she was very intuitive. She knew I was pregnant with my daughter before I did, I swear it. She always laid on my tummy in the bed and in the recliner and kneaded my tummy often. Suddenly she stopped and would only lay by my feet or head and was very calm around me. About three weeks after that started, I found out I was expecting. She stayed like that my entire pregnancy and then stayed at my daughter's side while she was an infant. She never got in her crib or anything, just laid beside it until she cried then meowed until I got in there. It was the sweetest thing and I really miss her.
