Oh my, there can be references to an age (date of birth) and a birthplace - that have nothing to do with identifying who the parents are. And vice versa.
First, in your example of a birth certificate, where are you going to post it on the parents' side? You can't post the child's birth to the parent's birth, can you?
If a couple had 16 children and you found 3 from here and 4 from there and 2 are unknown by name and 6 are from over over yonder - and 14 of them may have come from any of four different wives - who do you distinguish all of the sources for EACH of the 16 children - in both the CHILD's and the PARENTS's record?
What about a CA death certificate, which often only gave the deceased person's parents surnames? If a man, that generally give a surname to his mother - but which wife of the father? If a woman, this gives her maiden name (surname of father) and maiden name of mother - but who are her mother's parents and which wife of the father is she?
Or a headstone, which gives a middle name that suggests "almost certainly" a maiden name - and that's all you have - or contrary-wise you have 20 other sources for her, none of which gave her maiden name?
Or, in the case of trying to corroborate a 1700 (ie before censuses) published genealogy, all you have to corroborate her identity given in that Genealogy is that her asserted parents are, indeed, buried in the same plot with her?
On and on it goes, I could give a 100 examples of where the current structure in genealogy software is deficient and does not provide for documenting the relationship between people. One way to "cure" this deficiency is by Custom Facts - as mentioned. A lot of people just give up on the software and handle it with narrations in their notes - the "old-fashinoned" way.
I find it very strange that software seems to put so much emphasis on sources and not on how to document the three basic questions of genealogy:
1) How do we know (or can corroborate) that x is child of y and z (and vice-versa - ch of y & z)?
2) How do we know x is spouse of y - and when (and which wife husband is mom of which children)?
3) How do we know person A in a record at one point in time is the same person in a different record at either the same or different place at a different point in time?
Genealogy software just seems to ignore the basic questions of genealogy.