Each farm must decide what is best for them. There are very few absolutes when it comes to farming / care of livestock. Research, research, research and then make a decision that fits your needs, your farm's needs and your animals needs.
Here on our farm this is what we do:
Newborn kids whose dam didn't receive a Lamb Combo shot (CDT and Bo-Se combination for ruminants...both sheep and goats) will receive it at 1 week of age with a booster 3-4 weeks later.
If their dam received the shot within 6 weeks of kidding them we give the kids their shots at 3-4 weeks with a booster 3-4 weeks after that.
We used to give CDT and Bo-Se as separate shots but our vet custom compounds the Lamb Combo for us, which allows us to give one injection instead of two.
Do I recommend forgoing the CDT vaccination? I don't. I believe that it's an essential (core) vaccine that goats should receive. That said, there are plenty of farms out there who do not vaccinate. Make the choice, but make sure you know the potential outcome of your choice before you do.