Setting aside the initial question of "why would parents ever want to name their daughters with the following names".
Lexicography, and when a given string can be considered an official "word" or "name"
Let's start at the top:
What is a "word"?
In functional terms, a "word" could be defined as any specific combination of sounds that can be used to convey a specific range of meaning. When it comes to the written form, we then also talk about how this "word" is spelled. Usually, a "word" must be limited in size -- in written forms, for alphabetic languages, it's usually that set of characters between spaces.
Note that this "word" must convey meaning. I can decide that adsf8799zyih means "I'm going to the bathroom on Tuesday", but if no one else understands this, it's not functionally a word. If, however, a bunch of my friends and I start using adsf8799zyih with this meaning, then (at least for us) it takes on a quality of "word-ness".
What is a "real" word?
This word adsf8799zyih is made up. No dictionary will include this, not now.
Whether or not a word is "real" and worthy of inclusion in a dictionary is, honestly, a bit arbitrary. However, if enough people all agree that adsf8799zyih has a meaning that everyone can agree on, then it starts to take on social significance on a bigger scale. If enough people use this word, with the agreed-upon meaning, for a long enough time, dictionary editors might consider adding it to their next edition.
Now for the next part.
What is a "name"?
A "name" is basically a specific kind of "word", whereby the meaning of the "word" is a specific person.
What is a "real" name?
Much like for "real" words, whether or not a given name is considered "real" can be a bit arbitrary. Broadly speaking, it must be used by enough people as a name (to refer to a specific person), in an agreed-upon fashion (as in, "yes, this is the name of a person or other living thing, and it does not refer to furniture, or vegetables, or planets, or...").
In addition, the "name-ness" of a given label may depend on other factors. For Japanese, one of those factors is the Japanese government, which actually does impose certain restrictions on what kind of label can be used as an official "name".
→ This is where you're finding some of the resistance to your queries -- the Japanese government hasn't ever allowed, and likely never will allow, either 膣子 or 醜子 as official names.
→ Consequently, the effective answer to your initial question is "parents cannot name their children either 膣子 or 醜子 (and therefore the 'why' question is moot)".
As you've discovered, 膣子 does actually show up online as a "name" of sorts.
However, before we can take this as proof that 膣子 exists as an official name, we must investigate the provenance of this data: who gathered it, and where did this information come from, and what other details can we discover?
As others have noted above, the dictionaries that include 膣子 seem to all trace back to one or two apparently tainted sources, and thus they cannot be treated as reliable as proof of the "official-ness" of any name.
Looking more deeply at confirmable instances where 膣子 appears, such as Google searches, we see that the top-most hits are Twitter handles (where people can use whatever they want as their "name"), followed by the vandalized Jisho.org entry, and then several hits that appear to be Chinese rather than Japanese. None of this provides any compelling evidence that this is a "real" name for official purposes. We can add a Japanese particle to our search to ensure we're getting Japanese hits, such as this search for "膣子"+"は", but again we find only Twitter handles, Chinese strings quoted in Japanese texts, and mysterious hits that don't seem to actually include the "膣子" characters in this order.
All told, the evidence is that 膣子 does exist as a kind of name, but the evidence also shows that this is most likely a nickname or unofficial label.
Pulling together everything we can find about these two purported names, we can only conclude that these are not "official", and can thus never be used as children's official names. They might appear as nicknames, either applied by someone to themselves, or to other people.