My personal experience in
using QT apps is that they load / render perceptibly slower than the native UIs and QT applications are slightly bulkier in size (storage space and memory). This is kind of understandable as QT
emulates the UI through its own library (unlike, say, Lazarus IDE / Delphi GUI library that directly use the native UI library). However, size doesn't matter much today, and the very minor rendering delay is hardly discernable and doesn't reduce its usability in any manner. QT is a mature framework and especially suited for C++ developers. It's one of the popular ways open source developers choose to make their software available on multiple platforms.
As for "OS built around QT" you can try it our yourself - KDE Plasma ( https://kde.org/ ) is a GUI for Linux / xBSD that is built with QT, and on the mobile scene, Sailfish OS ( https://sailfishos.org/ ) also chose QT for its OS UI and recommends it for app development on its platform.
All said, often nothing outperforms the native libraries in terms of usability. (Performance, in terms of resource use, is a different matter as there are GUI libraries that are actually lighter on the system than the native ones, and even QT).