In answer to an earlier point, it was never the case that named parents had to attend a baptism (or even be still around or alive). A baptism register doesn't tell you who presented the child for baptism.
My 3x GGF was on a baptism register of 1823. He was named as father of an illegitimate son and his occupation was given. I'm fairly certain he wasn't at the baptism for 2 reasons:
1. Some time later he was subject to an affiliation & maintenance order for the child so was obviously not supporting his son voluntarily.
2. He was a member of a staunchly Catholic family and the baptism was in the C. of E. parish church.
