As a modern alternative, there are new, very slim immediate-mode UIs for tools out of the game industry which might not look quite as shiny, but render UIs very efficiently, with very little code to write and execute. For instance this dear imgui emscripten demo is a 325kByte download (1% of the Qt demo! and it gets smaller if you don't use all the different UI elements):
The UI is rebuilt every frame, and easily running at 60fps with very few drawcalls.
And people are doing amazing things with it:
The size is about 30MB, how much smaller would this get? Even a 50% shrink would be rather big.
In any case, I wouldn't exactly recommend building a blog using Qt this way. If you want to try building websites with QML, qmlweb is much better suited. I rather expect Qt+NaCl/Emscripten to be useful for larger browser applications, like 3D graphics software, games, scientific simulators, and so on.
There is a static size overhead of up to a few hundred kbytes for C/C++ runtime code which needs to be included in the asm.js file, and which normally lives in system dlls when running as native code, but this can be optimized by trying to minimize the use of C++ (e.g. iostreams introduce quite terrible bloat, better to just use printf). A lot of work has gone into emscripten to optimize the output size, also very recently (e.g. a linker pass which scans the code for duplicate functions and removes them, which sometimes helps for code which makes heavy use of templates).
It still bothers me that things are getting so big :D
So don't bother, just wait for it :-)
Having started programming on an Apple 2+ (64kb ram), I know what I'm talking about :-)
Aside from gaming, emulation and co , what are the business cases for emscripten ?