I have a similar situation, so here's some food for thought...
My 3x great-grandmother was born Lizzie Wade Rimes on October 7th 1868, the illegitimate daughter of Elizabeth Rimes. Banns were read out for a marriage between Elizabeth Rimes and Isaac Wade on December 13th, but the marriage didn't actually take place until exactly a year later, at the Peterborough Register Office.
The use of the middle name 'Wade' and then a quick attempt to marry Isaac strongly suggests Elizabeth considered him to be the father. In both the 1871 and 1881 census, Lizzie is recorded under his surname along with the rest of her legitimate siblings.
But when she married my 3x great-grandfather John Robinson in 1888, she uses the surname Rimes, and her father's name is left blank on the marriage certificate.
In 1948 when they celebrated their 60th wedding anniversary, a newspaper article described her as being the daughter of Isaac Wade. This was decades after his death, however, and obviously not an official document.
I have photographs of Lizzie and Isaac and in my opinion there is a resemblance between them. Isaac's features can also be seen in her descendants.
My DNA match percentage with descendants of Lizzie's younger legitimate siblings are consistent with Lizzie being a full-blooded sibling, which to me suggests that Isaac was in fact her biological father.
So like you, I'm left wondering why Isaac never claimed her officially, in what seems to have been a case of cold feet, only to marry Elizabeth and have many more children (thirteen, not including Lizzie!)