There are plenty of apps that use QT--probably the most mainstream one is Google Earth.
Now, look at me with a straight face and say, "And Google Earth has a great UI!"
To me, this is the problem with cross-platform UI. It starts from a mistaken premise: Windows and Mac or iOS and Android have the same basic UI. There's even a grain of truth to it. But it doesn't really work.
The example I love to use is French and English. They are, basically, the same language, right? They both have words, sentences, and paragraphs. They both have nouns, verbs, and adjectives. So if you just translate the words and move around the adjectives, you've got a French/English translator! It's that simple!
No, not really. If it's 100 degrees outside and you've just come from the outside and remark to a pretty girl "Je suis chaud" (literally, I am hot), she might very well slap your face. Because you've just said that you are hot as in, "Oh, baby, you make me so hot."
And those are the silly mistakes that cross-platform UIs make.
Take a simple one from Mac versus Windows: On the Mac, in a dialog box, the default button is always the right-most button. So you have a dialog box that says, "Are you sure you want to do this?" and the right-most button would say, "OK" and the button to the left of it would say, "Cancel." On Windows, the default "OK" button would be on the left with the "Cancel" button the right of it.
Alignment, again, is a question. I'm not sure there's a standard on Windows--I've seen things centered and I've seen them aligned right. On Mac OS X, there's a standard. Which means when Windows aligns them on the right like on the Mac, I'm always pressing the Cancel button.
So, yeah, you can use QT to have a cross platform application and it will work fine. And it's great, if you have an application like Google Earth, which has lots of great GIS capabilities so that the result is worth the pain. But, frankly, if Microsoft did an equivalent to Google Earth but made a Mac application that was "correct," I'd use it in a heartbeat. Because, all else being equal, I'd rather have an application that "speaks my language" to one that only sort of does.
Have you ever spoken to a tech support person from another country with a thick accent? That's the equivalent of using Google Earth on a Mac.