In the course of my work, I've spent much time researching at the county level mostly for assessors info., zoning, property records, tax id no.s, legal descriptions, surveys, etc. Thankfully, what used to be done in person can now largely be done online.
In my state, the county recorder rides herd on issuance of marriage licenses, birth and death certificates (what I call vital statistics) but that info is maintained by the state, near as I can tell. I don't know if that is typical of other states or not. The state website says they have all birth/death records after 1911 and all marriage/divorce records after 1947, while the counties may have older data prior to that.
However, it looks like the method for accessing that state info is formal with an application and fee process. I was thinking I could just punch somebody's name in and would get a relevant result, much as I would with a property ownership question. I don't know why the public information related to births and deaths would be harder to access than that of property stuff. That takes me to the original question of in your experience, is it normal for states to restrict it's access? Our state does have an online "repository" but that is for civil/criminal judicial rulings and such.
My interest in this is very casual and not related to genealogical research or anything. For example: "I haven't seen so and so for years, are they still living"? It's a case of my curiosity getting the best of me. Your suggestions are helpful, especially the local library angle.
Apologizing for the wordy reply, thanks again.