I may be remembering wrong. But I believe back when I used Qt a few years ago, the most common interpretation of the GPL license the free version used prevented you from deploying with a single static binary.
Qt is LGPL'd, meaning static linkage is possible as long as others are able to relink using other Qt versions. Providing your applications as object files is enough for this, no need to share sources.
You can technically deploy with a static linked Qt as long as you provide your compiled object files for download somewhere along with instructions for how to swap out the linked Qt with any other version of Qt. This keeps your code proprietary and honors the license.
For example, you must deploy as a static linked Qt on the Apple App Store, but since Xcode is free and no Apple dev account is needed to install an app on your iOS device, you can provide instructions for how any user could install your binaries with any version of Qt. Unlikely any user would ever do this, but by making the process publicly known, you honor the license (and you don't need to share your own source code).
Xcode might be without any cost, but the Apple hardware needed to legally run a copy of OS X (which also isn't free) - I don't really see how "Xcode being free" enters into it, as long as the software is distributed for iOS devices?
For the Mac app store, it might be different, as you need a Mac to access that anyway.
FWIW I think the issue here is that artificial limits on what code can be run on what hardware (legally) is in conflict with the (L)GPL -- and there's really nothing anyone other than Apple can do about it. Which is also why, as far as I know there's no actual legal way to distribute (L)GPL software on these locked app stores - there's no way for the distributor to actually honor the license, and so no way for them to be able to (re)use/distribute the code legally?
