It's a bigger issue if you're on a distribution like Debian Stable, which ships an ancient Qt version without security updates[4]. There, you get Qt 5.7.1 based on Chromium 49 (2016-03-02) with security fixes up to 54 (2016-10-19)... I'll probably drop support for that soon even if it's annoying for some Debian Stable users, but people really should stop using such old QtWebEngine versions.
Missing web features usually isn't much of a problem in my experience, as most sites still wait a bit before they start using them.
FWIW I agree something based on Servo would be cool, and as soon as there's some project making Servo embeddable from Python with Qt integration, I'll get my hands dirty to at least have a proof of concept!
[1] http://code.qt.io/cgit/qt/qtwebengine.git/tree/dist/changes-...
[2] https://wiki.qt.io/Qt_5.12_Release
[3] http://code.qt.io/cgit/qt/qtwebengine.git/tree/tools/scripts...
[4] https://www.debian.org/releases/stable/amd64/release-notes/c... - only mentions QtWebKit, but applies to QtWebEngine too