I’m not going to look up the law again, but I think that change was made in 2008, so you are incorrect that it would have said “parent”.
That’s exactly what this discussion is about. Changing it from “father” to “parent” changes the understood meaning from someone who is likely a biological parent to someone who is, instead a legal parent, and who in some cases, could not possibly be the biological parent.
Whether that change is in the interests of the child is what the discussion is about. A judge recently stated that the birth certificate was for the benefit of the child, so potentially significant changes will inevitably lead to discussion about who this change benefits, or whether the change might actually be detrimental to the child.
Legal changes are brought in. Much of the time they function well enough. Sometimes they have unintended and unconsidered side-effects, so reviewing changes as people become aware of them is a normal part of the process.
Realistically, the most common use of a birth certificate now is proof of identity. What then should it contain a record of and why?