Qt is LGPL licensed is it not? LGPL license means you can distribute your app closed source, so long as the user can swap out the Qt implementation. This usually just means dynamic linking against Qt so the user can swap the DLL. The rest of your app can be kept closed source.
On iOS and Android the situation might be a bit more complicated, but this discussion[0] seems to say that dynamically linking would also work there.
Qt doesn't require that but even if it did writing it 6 times is vastly more expensive. People would just rather spend 500k on writing it 6 times than 5k on a license because they are somehow offended at the notion of paying for dev software or tooling.
It's a major reason UI coding sucks. There is no incentive for anyone to make it not suck, and the work required to build a modern UI library and tooling is far beyond what hobbyist or spare time coders could ever attempt.
Also I think you can deploy to all those things with Qt.