Do most even remember it? The fact is there, yes, but humans don't operate on facts alone. When it comes to the conception of life most people point towards the process that creates it, not the fruit of the labor.
I'm speaking under the impression of general consciousness. Despite how they're innately connected, most people view birth and intercourse as VERY SEPERATE THINGS, as the latter is treated more recreational than ever as birth control rises in use, and the potential bodily harm that it causes is proliferated so much that it's garnered a reputation that rivals the likes of drugs and violence, hence the popular phrase of "sex, drugs and violence", as their commonly seen as a trio.
I'm not saying birth doesn't entail bodily harm either, but it's overshadowed by the occasional of literally birthing new life. It is to the point where the pros overrides the cons so much that it's considered widely as "worth it".
But as a side note, do keep in mind that I'm speaking this from personal observations of popular culture and conversations I had within my acquaintances. This is how sex is viewed, not as a conception of life, but as a VERY ADULT way of pleasuring oneself.