Statutory rights as I understand them to be are laws written to offer protection, According to dozens of web sites regarding parental rights there are laws in place to enforce those rights. This example site lists various situations where parental rights are defined.
https://www.kabirfamilylaw.co.uk/what-rights-does-a-father-have-to-see-his-child/
This is going to be a problem isn't it, (if not well and truly a problem already!).
On the other recent thread in this section of the forum I mentioned the professor whose paper informed me, (albeit many years ago), that there were no statutory parental rights in the UK, and she said this situation contravenes some sections of human rights legislation, such as the right to a family life.
I then said your argument, (should you disagree, as you obviously do), is with her, or her opinion.
We can run round in circles to the end of time as to when something described as a right, (such as the "right to send your child to school"), is really an obligation, rather than a statutory parental right, (because a parent has no right to refuse of course), but it will be a bigger waste of time than my asking you why you feel unable to support my call for the very meagre statutory parental right (called a "rebuttable presumption in favour of contact for decent parents"), that would mean those decent parents who have split up both continue to enjoy the protection of their role in the child's life the one the child resides with continues to enjoy under the "common law rights" that exist in this country.
I know that's a long paragraph, and apologies to anyone reading it who cannot make sense of it, though what it boils down to is that both divorcing parents have at least some statutory protection of their role in their own children's lives, and there has then to be a "good reason", should the other parent (/residential parent), wish to exclude them.
At the moment, there are professionals working in family law who state this: "Even if the reason why the residential parent is behaving irrationally when excluding the other parent, it is offensive for the courts to intervene if the child knows their residential parent does not wsh them to have contact with the father"(/non-residential parent).
The judge whose responsibility to conduct a review of UK family law seemed shocked by the response he got to his list of questions, (those giving him the view irrationality could/should rule cases of obstructed contact with children worked at Leeds University), but the law in place today allows this kind of thing to go on unchallenged.
To give you an example in one calendar year in the UK, (a good while ago now), two women were jailed for obstructing contact with their children's father, and flouting court orders saying the contact was in the child's interests. One women changed her behaviour as a result, and the other did not, and this was considered a failure overall.
Contrast this with the situation in France where a British father approached their family court system in order to get to see his children, (where his ex wife had moved to live with her new partner/husband). That non-resident British father was granted a contact order by the French courts, and the judge presiding told him that if the mother flouted the court order he should not come back to the courts to find remedy but simply go around to the police station, (or "gendarmerie"), and an officer would accompany him to see that the contact order was followed or enforced.
This sort of action by the police is impossible here, and I've listened to fathers in this country you have had literally hundreds of court appearances trying to gain access or maintain contact with their children, and the residential parents have repeatedly flouted court orders without any repercussions.
Never mind, as the thread title says or indicates, "so many people wish to deny decent parents any statutory legal rights, (or even the most meagre meaningful parental rights), I'm sorry for you but there is no hope of change here whilst your fellow man or woman wont support even a small (though fundamental) change".