I have never once tried to stop my children's fathers from being involved in their lives, I actively encourage it.
He left me. He chose not to contribute financially. He chose not to be present at the birth. He chose not to see his baby. I simply chose to not put his name on a certificate, which is easily rectified by him going to a solicitor. If he was interested.
I was very aware that the situation might change, so I was always very open about her father, and when she requested to see him aged four I would spend money on public transport and take her to him. She simply wouldn't have seen him unless I paid and did the four hour journey each way, in my wheelchair with a four year old.
When she stayed over, it was me that provided the money and clothes she needed, as well as the transport. When she wanted to speak to him, I paid for the calls.
When I became too disabled to care for her properly, she went to live with where she was better off.
My son's father had 50/50 parental rights after we split and we worked together on everything. We still do, the only time I ever stopped contact was when I had concerns about my son's well being as his father's girlfriend was physically and emotionally abusive toward him, and emotionally abusive towards my DS. I cried for my son, because it felt so wrong to do, but it was the only way I could protect him at the time.
People make some bloody strong assumptions based on one piece of information. So what if we don't put their name down, they don't usually bother attending the registration anyway, so why give them rights when they have no interest other than to get whatever benefits them, like a free holiday to mess about while the mother is giving birth and caring for the child they have abandoned?