I was unaware that being a spouse carried more rights than being a biological parent, so I am certainly one person whose opinion has been changed by this thread.
I suspect it’s a common misconception as father is more generally used nowadays to mean biological father. But when the laws were written, being legally married was more significant. It may have been unspoken that the spouse and the father were not always the same man, but it is clear in the law that the mother’s spouse could be added readily, while listing the biological father was actually more complicated.
I would question whether it might be better to go back to first principles and work out what information is useful to the child to have on that paper, and why, but if it has always been the case that a spouse can be added, without question, then adding the spouse, whatever their sex, may well have been “in the spirit of the law” in a way that I hadn’t appreciated before.
I would be quite glad for my daughter to be on the birth certificate if she was married to the mother, in some format or other. I can’t see what harm that would do and I can see that it would be useful in some circumstances. But it might also be useful to have the biological father listed as well. So I’m somewhat on the fence about who should be listed and what format that should take. This entire conversation has opened up for me just how complicated parenthood has become.