A comb is doing the job if –> plenty of fur on the comb. Little or no fur on the comb –> not working.
Metal is better for combs. https://youtu.be/3QDm_7_T49Y
What about a plastic brush? Among other tools, I use a plastic brush for long-haired cats when I’m blow-drying them. I also use it on my hair. Double duty.
For your cat-bathing tool kit: The Wet Brush 2 Pack! Blue & Pink, Value Pack!
For your daily grooming tool kit: Andis Pet 7-1/2-Inch Steel Comb (65730)