I don't know about Cook and Carrie, but I'm pretty sure Daughtry writes or co-writes some of his songs. Kelly has written or co-written songs on all four of her albums to date. Not every song, but about half of all her material so far. Kelly wrote her Grammy-winning hit 'Because of You' when she was only 16. Not only was it a smash on Pop, but the Reba-Kelly duet version was a smash in the Country genre.
However, Kelly didn't co-write 'Hook Up'. AI judge Kara DioGuardi did, with a couple of other songwriters.
Kara has written a number of Kelly’s hits