In my local council, I had to register in order to be able to take DD there at all, so it is definitely voluntary and you need to be proactive to go and see them in some places.
I agree with what several others have said, in that sometimes they are a great help, other times not. You sound to me as though you have a very rational head on your shoulders, so I can't see that visiting your clinic would cause you too much alarm in any case Having said that, there's no point in visiting a chn who does or says absolutely nothing to help you.
I took Natalie for the first 6 months, then a couple of times after that, mainly when I had questions. I could have seen my GP but the clinic was closer and more convenient at the time.
When she was 4-ish months, they suspected a lazy eye and so sent me to the eye specialist when she came to town. Cost me nothing, was something I hadn't noticed myself, turned out her eyes were perfectly fine anyway. But I am so glad we checked because if there had have been something wrong it would have been easier to address earlier rather than later, KWIM?
Good luck with your decision(s) - there are so many to make as a new parent! I HTH a little.