The web has legendary backwards compatibility for widely-deployed features - you can still correctly view the original Space Jam website from 1996! That's a website over 20 years old.
Not bad. I remember tables and sliced images were popular method of designing webpages around that time.
I recently saw a benchmark where the C2 engine in Chrome outperformed a competitor's native engine on desktop Windows, and approximately equalled another which compiled to C++. This pretty much confirms to me that the performance argument for native, or this idea that "HTML5 is slow", is totally dead now. Having a native engine does not guarantee good performance, and modern JavaScript JITs are incredibly potent. For years I've already noticed that almost every performance complaint comes down to hardware limitations (e.g. GPU fillrate), and people simply knee-jerk blame HTML5 without understanding what the real problem is. So as far as I'm concerned, we're there: HTML5 has native-grade performance now. There's nothing significant to gain by a native port.
You say that, but there is an overwhelming amount of people who say otherwise. A lot of C2 developers have switched to Unity because of performance. Who should we believe?
Performance aside, I think C2 and C3's biggest problem is third party wrappers. I haven't found a wrapper that I haven't experienced some trouble with. If C3 was native, you wouldn't need to rely on HTML5 wrappers. Construct is fantastic for browser games, but it's a real pain trying to get it to work on other platforms.
My prediction is that browsers will stay, technology will evolve and we'll see more full featured applications written in web languages. That doesn't mean that they won't be also available for the OSs (through integrated HTML5), but the "write once deploy everywhere" trend will get a bigger audience as technology matures.
That's possible too.