I know we will all find an ancestor who was illegitimate, a baby born to an unmarried mother with no father mentioned. A distinctive middle name may occasionally be mentioned, which can give a clue, or the putative father was even named, but often the baptism was just for example, "Samuel Davis, son of Ellen Davis, baseborn". Bastardy bonds are helpful, and maintenance orders etc, but there may not always been one made, and the mother raised the baby with help from her family, or she married the father/another man perhaps months or years after the birth of the child or children.
In advances in DNA testing it is getting easier to trace fathers of illegitimate children. And of course the baby may have been born illegitimate but was baptised after the parents married, or occasionally the man the mother wed may have just said he was the father to save face.
But sometimes I wonder if the anonymity of the father is what is compelling. For instance my ancestor Mildred (known as Amelia) Wickham was born in 1801 in Twineham, Sussex, to an unmarried mother Mary Wickham who was born in Bolney in 1779. So far I have never found any hint as to the baby's father. Mildred married in Bolney in 1818 aged 17.
I have an ancestor Phoebe Johnson born in 1807 in Rochford to an unmarried mother Sophia Johnson. Sophia wed Samuel Coote in 1809 in Rochford, and he was soon subject to a settlement examination, and it says he was recently married but no mention that he was Phoebe's father.