As a single mum with primary care of my ds, I decide everything on a daily basis and do not refer to ds' dad. DS lives with me and sees his dad for a few hours a week. Ex' contribution is mainly financial, he has ds about 20 nights a year. His choice.
My 'greater rights' over the absent father are that I get to raise my son with decent values, have the opportunity to instill ds with a decent work ethic, teach him the kindness, fairness and equality that I regard as important. Ds & I chose his school, ex was not involved.
Ex has never done a school run, a parent's evening, a gp or dentist run. When ds was in paed ICU, he couldn't be bothered to get the car out (he'd been drinking) and said he was 'sure I could cope'.
I have never worried about ex's legal rights as a parent because he is too lazy to make a fuss about anything. I take ds abroad whenever I wish and generally I regard ex's views as irrelevant. He is a lazy and selfish father.
However, I accept that there is value in ex being able to, IF IT PROVED NECESSARY, go to court and exercise his rights as a parent, simply because it gives ds a second parent to fall back on - for example if I developed an addiction or chose a dodgy boyfriend etc. Ex may be a crap fall-back option but he is better than nothing.