I’m going to address your subject question first: What is the point of third-person limited? Third-person limited is my favorite POV because it has the potential to be incredibly intimate. It puts the reader unequivocally inside a character’s head, with access to thoughts and feelings that the character might never otherwise choose to reveal. In first person, the narrator is always present between her own thoughts and the reader; there is always an implicit filter, an implicit editorializing. In first person, the narrator implicitly gets to choose how much of herself to reveal; she can be honest, or she can be cagey. In third person, the narration can lay the POV character utterly bare, whether she likes it or not.
(The narrator presence in first person can be useful, of course, as when you are aiming to write an unreliable narrator story. No one POV is inherently better than another; each has strengths and weaknesses for different types of stories.)
I recommend this book a lot for all kinds of reasons, but take a look at Patricia Highsmith’s
The Talented Mr Ripley for a master class in what third-person limited can achieve in the way of narrative intimacy. And, incidentally, there are very few women at all in that book, which brings me to your other points.
For one thing, it makes pronouns confusing as hell.
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The two hacks I’ve noticed authors using to get around this are either, bending over backwards to make sure that interactions always happen between one man and one woman; or giving all the characters very short one-syllable names.
This is an odd assertion, and perhaps just means you haven’t read enough third-person limited work. For one thing, wouldn’t first person have exactly the same issue any time your character is interacting with two women or two men at the same time? For another, competent writers structure their scenes and their sentences and their action beats so that the writing is smooth and it is always clear who is speaking or acting.
And now I’m wondering, if you’re limiting knowledge to a single character anyway, what’s the point of this POV and why is it so popular?
Again, does first person POV not limit knowledge to a single character? You are ascribing problems to third-person as though they are unique to third person when they simply are not.
In addition, third-person limited only means that you remain in a single character’s POV for the duration of a scene or chapter. You can switch to the POV of another character in another scene or chapter, if your story requires it. There are also books in which some POVs are first person and others third person. (Andy Weir’s
The Martian is a recent popular example that leaps to mind.)
When I needed a short same-sex flirting scene, I started tripping over pronouns. I've written romance scenes before and never had any problem (either first person or 3rd person hetro), but without the simple he/she pronouns it quickly became comically difficult.
Sarah Waters manages it—
The Paying Guests is third-person limited and contains a healthy spoonful of sex scenes between two women. Mary Renault’s
The Charioteer is pretty much a book-long flirtation between two men, and her writing is flawless and gorgeous.
Most of the scenes I’ve posted in Share Your Work over the last couple of years (Historical Fiction section) contain conversations between women. Most recently I posted a sex scene (R-rated) between two women. It
was extremely difficult to write, but the pronoun issue was not at all what made it difficult! If you like, you can read it and tell me if you find it awkward, the way I identify who is who. None of the feedback I’ve received on it cited that as an issue.
I'm just surprised that multiple first person POV isn't really a thing. Off the top of my head, the only book I can think of that uses it is Dracula.
Tocotin already mentioned that multiple first-person is indeed a thing. In addition to the books she mentioned, Vera Kaspary’s
Laura is one; more recently, Barbara Kingsolver’s
The Poisonwood Bible; more recently still, one of my very favorite books, Elizabeth Wein’s
Code Name Verity. That’s just off the top of my head; a little bit of thought, I am sure, could turn up many more. My understanding is that many romances are written this way as well.
tl;dr, go forth and read more! See what different authors have done with different POVs. Third-person limited is extremely fruitful and powerful. Might there be some stories for which another POV is a better choice? Sure—but don’t dismiss it out of hand until you fully understand what it can do. There is a reason that it is commonly used.