"Does anyone think it'd be a good idea for browsers to support more than one toolset?"
Some people do. I do. But it seems to be a minority opinion; most web developers seem to live in this weird cognitively dissonant state where the HTML DOM+CSS is always the right tool for the job because it theoretically allows for platform-independent layout to "any" browser while then spending most of their time dealing with getting their layouts to actually work on about a handful of real-world browsers which all treat the same layout code differently (in ways from subtle to large); resulting in piles of frameworks, pre-processing systems and general hackery to get everything working, mostly, most of the time.
If there were a second toolset that were more rationally designed to solve the real-world problems of modern web apps, giving you layout via binding similar to what you see in Adobe Flex, WPF, Qt/QML, etc (not advocating any of those as the specific answer, just stating that I think they are all individually more sane than HTML/CSS/JS for app/UI layout) and just accepted the fact that the vast majority of websites are designed to be laid-out in a fairly constrained way (while still allowing for responsive layout for different sizes/dpis) I think web technology would be a lot less terrible.
And just to get it out of the way, there are some good hacky solutions that help the problem I described, like React.js, Angular, Dart, etc, but they are all built on a shaky foundation which always manages to show through because we're stuck with HTML/CSS/JS.
I used to believe using something like the tools you outlined would be easier until back in 2004 I spent 6 months porting my naitive windows application to apple. I scrapped the whole thing and started rebuilding on the predecessor to xulrunner, rebuilding mozilla and using XUL was great until I started to need graphing and different fluid layouts that I realized HTML is so much better for cross platform as more people are spending more hours every day making it better on more platforms and devices and it really is write once run everywhere once you move your native app to the server - at the end of the day you are going to spend countless hours tweaking for the different target OSs anyway - the web with HTML / CSS / JS are better at this than any other native solution...
[update] we ported our native c++ components to xpcom interfaces and rebuilt the frontend in 4 months allowing us to launch our product simo health - later purchased by RevolutionHealth 4 months later... I still as recently as 3 months ago receive emails from past customers asking for updates.
Some people do. I do. But it seems to be a minority opinion; most web developers seem to live in this weird cognitively dissonant state where the HTML DOM+CSS is always the right tool for the job because it theoretically allows for platform-independent layout to "any" browser while then spending most of their time dealing with getting their layouts to actually work on about a handful of real-world browsers which all treat the same layout code differently (in ways from subtle to large); resulting in piles of frameworks, pre-processing systems and general hackery to get everything working, mostly, most of the time.
If there were a second toolset that were more rationally designed to solve the real-world problems of modern web apps, giving you layout via binding similar to what you see in Adobe Flex, WPF, Qt/QML, etc (not advocating any of those as the specific answer, just stating that I think they are all individually more sane than HTML/CSS/JS for app/UI layout) and just accepted the fact that the vast majority of websites are designed to be laid-out in a fairly constrained way (while still allowing for responsive layout for different sizes/dpis) I think web technology would be a lot less terrible.
And just to get it out of the way, there are some good hacky solutions that help the problem I described, like React.js, Angular, Dart, etc, but they are all built on a shaky foundation which always manages to show through because we're stuck with HTML/CSS/JS.