I'd love to use this but a key problem seems to be that they don't get updated as soon as a security fix is released, which for browser engines is quite often...
Then there is the issue of "stable" Linux distributions (mostly Debian/Ubuntu) which never get those updates to you unfortunately, and don't seem to care about those being security-relevant either. Not much either qutebrowser and Qt can do about that sadly, but you can install Qt from somewhere else, e.g. from the PyQt binary builds if you don't mind losing proprietary codec support: https://qutebrowser.org/doc/install.html#tox
As soon as a new Qt/PyQt is out, there is usually also a new qutebrowser release bundling it for Windows/macOS releases.