You simply can't create an app with a high-quality, Mac-conforming, polished UI with cross-platform tools like Qt. The apps always end up with small but noticeable differences and peculiarities compared to 'native' Mac apps.
You can argue about the merits of wanting such a UI, but given that the Monodraw developer does, creating a Mac-only app is the only option.
I usually care about functionality more than about small noticeable differences between platforms. "Not available at all" is way worse in my books than "doesn't look like 100% native".
Sure, any cross platform UI can be a trade-off. The question is what is more important, to leave out users of all other platforms by making the UI look more native, or to reach more users.
There's more to "look and feel" than just look. Qt's been using native rendering APIs for years, but they still have to emulate the native functionality, and when they get it wrong that's a lot more annoying than getting the look wrong.
I'm currently rewriting my Mac application. Its prototype was written in Qt, but I'm now dropping Qt for several reasons:
1. I demoed my application to my friends and they all complained that it didn't behave exactly like a native Mac application.
2. Qt5 has a lot of UI bugs on Mac OS X.
3. The LGPL license of Qt may not compatible with Mac App Store [1].
4. I could buy the commercial license of Qt, but it's $215/month for Mac OS X. I don't know if my app is going to sell at all, so I can't afford that kind of burden.
#3 is Apple's fault. I'm not using OS X so I don't know about their installation policies. Do they require to use their store to install applications now? In the past you could just provide packages on your own.
As to 3), unless you are making closed source changes to Qt, I can't think of any way that the LGPL could make your app incompatible with the Mac App Store.