The offline installers seem to work:

http://download.qt.io/official_releases/qt/

At least, after disconnecting the internet connection then ignoring the subsequent error (ironic for an "offline" installer!), it doesn't require a Qt account.

That's exactly what I ended up doing, but I hope we'll agree having to do tricks like that in order to use an installer is not... ideal

Very much agree.

For now we (sqlitebrowser.org) will keep with the easy approach of using the official Qt installers.

If Qt does something even further dumb though, we'll likely move to compiling Qt ourselves. And probably then make installers (.msi/.dmg) for anyone else that wants it too. ;)