I understand your reluctance, but from a developer time perspective it may make sense to use a cross-platform toolkit even if the users isn't going to enjoy it as much.
Ultimatively it comes down to economics: are you willing to pay five dollars for a native app or 1 for a cross-platform one?
That's precisely my point though - I think the software market has reached a point where developer laziness like this simply won't fly.
There was a time when the functionality of our products compared to the status quo (e.g., word processing vs. typewriters) was so ridiculously skewed that we could get away with bloody murder. And we did. We invented insipid modal UIs that jerked users around the app. We invented gigantic toolbars with hundreds of vague icons because we were too lazy figure out how to let users access their most used functions quickly. We created unforgiving apps where just glancing at it wrong resulted in data loss. We abdicated our responsibility to make features accessible, and instead printed large manuals and tear-out cheat-sheets, and made fun of people who couldn't handle the information overload.
That era's long gone. Look at the App Store - it's a parade of failed apps eviscerated by users for bad UI. It's a gallery of obscure apps that never made it out of the gate because they didn't put thought into their UX. Now look at any of the top apps (in whatever way you define it: top grossing, most downloaded, highest reviewed, whatever), and you will see that one main common thread that connects is that their UI doesn't suck.
People's tolerance for bad UI has decreased rapidly for years, continues to decrease, and the number of places where you can get away with it is rapidly shrinking. On the desktop you might still have that much breathing room - on the hyper-competitive winner-takes-all arena of the App Store, you have no chance.
As a side note - I highly doubt Qt will save a developer enough time to make the difference between a $1 app price vs. a $5 app price. There are so many low-level fundamental UX differences between iOS, Android, and any of the other mobile platforms that full abstraction is simply not possible in the way that we have been able to do on the desktop.
What does "having a UI that doesn't suck" to do with using native controls? When I look at the top 20 paid apps (germany), 13 of them don't use a single native control (most of them being games). Most sucking applications in the App Store suck even though they are using native controls.
I understand that the UI will not be native, but it is very possible to create nice UI with Qt. Just look at the N9 and the apps therein, which uses Qt only for the UI. With QML/QtQuick, it's even very easy to build nice UIs.
Ultimatively it comes down to economics: are you willing to pay five dollars for a native app or 1 for a cross-platform one?