That's mostly because of "identity theft", at one time they were indeed "public records", which anyone could request. But you can see the basic conflict between counting on a BC as proof of identity and citizenship, and allowing ever Tom Dick and Harriet to get a copy of anyone's certificate. The reason for the restrictioin on Marriage certificate is less clear.
That is so if you want to get a CERTIFIED copy of the certificate. But I know you can call, or go to the County Clerks office and ask if there is a record of so and so's marriage. I have done so. I have also gone to the court and asked to see divorce records. Although I had the file number on these. Not sure if you just have a name if they can locate the file for you.