Apart from any moral responsibilty a person might have to notify the state, let me ask this:
What legal responsibility would a person have?
What legal responsibility would a person have?
Legal responsibility would be determined by the locality where this occurred.
You should determine what that is before you engage in activities that run afoul of local laws.
Generally, you have the right to choose or refuse medical care, calling 911 is not a legal obligation, although some have tried to make it so.
Birthing professionals are required to notify the state of births, in an unattended birth, there is no one present with a legal responsibility to register the birth.
On burial? Different states have different rules on disposal of human remains and where they can be interred. Depends on land use regulations. Burial on family property may or may not require a permit.
You can't even fix your own toilet, w/o a licence and permit in most places. What makes you think they'd allow you to do babies. So far, you're allowed to feed yourself, and wipe w/o license and permit. Soon you'll need training, license and permit to do that.
Negligent manslaughter.