Adding to what @OldUser mentioned, the passports are issued by the Department of State. However, the information isn't registered with USCIS and USCIS is the ultimate issuing authority for citizenship. So, yeah...that's why you want the CoC. It's a weird one...kinda like pictures or it didn't happen - get the CoC or it didn't happen, irrespective of a passport.
If the passport is lost or stolen after the age of 18, the kids will need proof of citizenship to replace it.