So there are three parties.
What happens if the relationship breaks down?
Its bad enough with two parties who have parental rights. With three do we think there will be the same level of problems, less problems or more problems - which pose a risk of psychological harm. Children need stability. Do we think custody disputes between 3 or more parents will be just fine?
If we can have children with 3 people with legal parental responsibility, why not 4 or 20? At what point does it change from being a parent/child to owner/possession relationship? What has happened with communities where children have been raised with 'multiple' parents?
The issue is the more people you throw in the mix, you weaken bonds of responsibility and add layers of not really knowing how you fit in. We know from children who are adopted biology remains a fundamental issue in terms of understanding who they are and where they come from which can not be ignore. Erasing a child's ability to access this information removes something from them.
The needs of the child always come second to the wants of the adults in these situations - and thats the biggest red flag going.