I think there is a little "super special bubblegum princess" to his romance. That is, there are moments where I feel like the writer is trying too hard. But you know something? The guy is a catch in DAI. I'm tired of being lied to, abandoned, and generally feeling like a chew toy every time I roll a straight female character. The Trevelyan "type" doesn't come easily for me but I'm going to grit my teeth and see if Trevelyan/Cullen is something I can make work. Because I do want the nice, stable guy.
It sounds from the rest of your post like you haven't started his romance yet--are you basing the part in bold on watching it through on YouTube or something? Of the other LIs whose romances I've looked into at all, most (all?) call the PC "my lady" or "beloved" or "my heart" or what have you, whereas Cullen just calls you "you" in person or by your first name to his sister. He shows or tells you often that you're important to him, but never in a flowery or overwrought way. He's emotionally supportive and physically affectionate, but so is Garrus, and no one ever goes on about how his romance is made of cotton candy.
Aside from the occasional awkwardness (which I can agree is overdone by fandom but which I really don't think was overdone in-game--and again, Garrus), the only remotely cutesy thing I can think of Cullen saying is "yours is the only attention worth having," which (1) I wouldn't trade even if it is syrupy because it made me blush IRL for what may have been the first time in years, and (2) this is subjective interpretation, but it seemed like an honest, annoyed-introvert statement on his part that he realized halfway through was coming out smoother than expected, like the "you're not distracting" bit in DA:O. 
I just don't see it. Maybe everyone I know IRL is secretly a former Barney the Dinosaur cast member or something and my sense of this is weirdly calibrated. Or maybe it has to do with a character in this fandom being interested in a fem PC but not hypersexualized, broody, or a liar. (And that's not a knock on the other LIs. I do love Isabela/Zevran/IB, Fenris/Anders, and Alistair/Anders/Blackwall, respectively. Solas I can take or leave. Well, and I love Anders as a character but haven't tried his romance and don't think I'd like it.) Having never played or YouTubed Merrill or Josie's romances I can't speak to those, and maybe they've got a point with Leliana's butterfly eyelash thing, but the "sugar rush" reaction to Cullen confuses me unless the person saying it is looking at fanon instead of canon.
Do people say it about Cassandra, btw? Not much about her (as a romance, as opposed to a Ripped, Bear-Punching Imaginary BFF) seems to come across my tumblr dash.