For this question I'd need someone who's as interested in biology and endocrine systems as I am.

On the one hand I was wondering why we need to watch our prolactin levels

I mean sure yeah grossness leaking from the chest and stuff but that's easily controllable surely.. I got "You will be Infertile... maybe you will get headache" Hmm yeah I don't care doc my infertility was already a given.

I conversely looked at what happens if you no longer have any prolactin or testosterone in your circulation at all. hypoprolactinemia,
I saw that such a condition exists has a number of unique effects.

Your Pubic hair falls out.
Your Armpit hair falls out.
Your Facial hair falls out.

Really? Wow! why arn't we blocking prolactin!? screw normal "ideal" levels Hey if it helps me avoid hours of electrolysis i'm totally game... XD
I can't find any studies on this... It's just mentioned as a symptom of the condition. Hmm I mean I can see some difficulty in blocking prolactin completely as you'd normally do it with something like lots of dopamine, which might make you paranoid and hallucinate.

because elevated prolactin might be a symptom of a tumor or too high estrogen levels
https://health.google.com/health/ref/Prolactinoma

Well...there are risks of eye and vision problems for one.
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And if all of your body hair is falling out...even those tough old facial hairs...I'm guessing your head hair and eyebrows wouldn't be immune to it either.
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I couldn't find much on whether any of the symptoms would be reversed when hypoprolactinemia is reversed to normal.  If they are, then your facial hair comes back.  If they aren't...if you lose hair in the wrong places you might be extremely disappointed.
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Any way you slice it, it's a pretty risky way to try to get rid of facial hair.