I do WW and now do it at home (was going to meetings but stopped in March). To me CC and WW are almost alike. WW has some funky formula that takes in account the calories, fat and fiber of a serving and that equals a point amount. Fiber is capped at 4 so people can't add more fiber to something to lower the points value (I could go on lol but I'll stop there) I've done both but I tend to become obsessed more with a bigger number...dunno why but it just is lol It's working for me and since I've totally changed the way I eat...lean meats, healthy fats, whole wheat products, fresh fruit and lots of fresh veggies, etc....I know I won't be going back to my old way of life. It's just what I do now.
I do however track my calories for a week every few months on the daily plate to get an idea of what area in my diet I need to tweak...sodium, eating too much carbs, not enough protein, etc. I'm a carb/salt nut and sometimes I indulge a little more in those areas even if I stay with in my points or calories.
If keeping track of points is working for you then I say stick to it. It's certainly a lifestyle change no matter if you CC or not
As for the zero point foods (which is usually a serving of a veggie, 30 cals or less...plain with no additives) or any double/triple serving...if you add 0+0 it does not always add up to zero
So you'll wind up counting it some way if you over indulge.