I've been lurking in this thread for so long (damn you dread wolf!), and enjoying tremendously, always too shy to take part in. 
Andaran atish'an! It's always good to see another long-time lurker-turned-poster (although I don't always respond either, because I'm also very shy
).
Solas was one of the last LIs added to the game, - if deadline and budget were not extended, we would never see that side of him - yet he seems so loved (or maybe its me that Im so stuck with him, but i think he has made his LI power known and well established, he has a very active and passionate fandom
).
I know. It's kind of amazing, right?
I mean, I love him, but I also know what sorts of LI's most girls tend to go for, so I was sure I was in a very small minority until I came here. I was pleasantly surprised to learn how large and how dedicated Solas' fandom was, despite how limited his romance content and budget is. (I mean, he's not exactly model-gorgeous, he's only available to female elven characters, and his romance ending is so sad no matter what you do. I didn't think so many people would like him with all those restrictions.)
It was a slow fall for him as I got to know his character (these are the worst - the longer it takes you to fall, the longer it takes to be forgotten).
Same here!
Although, to be honest, I didn't think that much of Solas when I first saw him. I kind of thought he looked plain and boring (I mean, he's bald, he's pretty okay looks-wise, and he dresses in plain beige and brown wool clothes when he isn't wearing scruffy, frayed "hobo apostate" versions of armor), and I didn't think there'd be much to his personality besides being intellectual, serious, and logic-based. Boy was I wrong on that front! And the more I fell for his personality, the more handsome he became to me. 
What is it that makes a LI so overwhelming in a game, as he is?
What was it for you that made him so special?
It's hard to say, but I think part of it is how calm and intellectual he is, and another part is how he brings something new to the table.
Like you said, most romances for females are kind of similar. You have your knights-in-shining-armor who've never truly lived or loved until they met the PC, now they feel so alive and can't imagine life without you (Casavir from NWN2, Kaidan from ME, Alistair from DAO, Cullen from DAI, etc), or you've got your "lady-killer in love" (Gann-of-Dreams for NWN2: MotB, Zevran for DAO, etc), or even former slaves/heartbroken badasses whose former love was killed and they've slowly been picking up the pieces of their shattered lives and now they feel you're their new life (Aaron Gend from NWN, Valen Shadowbreath for NWN: HotU, Fenris from DA2), and as much as I love them (I've very rarely encountered a romance I didn't like), after a while it becomes a similar song and dance.
But you don't often get a romance where the character's appeal comes from him being so intelligent and refined. And even though I said he looked kind of plain in the beginning, in the end I also really like nerdy, intelligent, intellectual characters, but you don't often see them as a romance in video games thanks to our anti-intellectual culture.
Solas' appeal (for me) doesn't come from being model-gorgeous or a knight-in-shining armor or unfulfilled without the PC's love, it just comes from him being his intelligent, nerdy self. 
Plus I love all of his knowledge of the Fade and elven history and lore, and all the possibilities the Fade can bring. (And the Fade has so many possibilities for so many cute interactions since anything can happen in dreams!
)