I question the premise of your question. Perhaps you are just looking in a skewed dictionary:
The perfect girl. She will light up your life from the moment you meet her.
She's smart but not nerdy, hot but not slutty. Beautiful body and a gorgeous smile, and always up for a good time. A Juliet will be the best girlfriend/friend you will ever have, she's the girl you will want to make your wife.
Sexy, athletic, intelligent, loving, and knows how to party. She may seem intimidating, but that is only because she knows what she wants, and knows she needs a real man.
Sure, the source above is Urban Dictionary, but at the very least it reflects actual usage to some extent. The entries are created by users, and there are several entries for Juliet, which might indicate a significant amount of common usage.
As I mentioned in my comment, I've been searching ngrams and the Internet in general in different ways, and despite the situation in the quoted dictionary, there seem to be plenty of uses of "my Juliet" or "she's my Juliet", etc., and it doesn't seem like using Romeo in the same way is significantly more common.
Also, Juliet (from Wiktionary)
- A woman who is or is with a great lover.
- By analogy with the Shakespearean character, a woman who is in love with a man from a family, party, or country opposing that of her own.
It seems like the "reputable" dictionaries that come from the age of print do not have a definition for Juliet equivalent to their definitions for Romeo, but the crowdsourced online dictionaries do. Perhaps the culture on the two terms is currently in flux, and the older dictionaries are not caught up.
Interesting source (Bartleby): Juliet
Daughter of Lady Capulet, and “sweet sweeting” of Romeo, in Shakespeare’s tragedy of Romeo and Juliet. She has become a household word for a lady-love.