One notable major site which uses Flash and which almost guarantees that Flash will not die out any time soon is Youtube

I use the Youtube website every day on my iPad (I can't be bothered to install the app). It works find and there is no Flash.

I spent yesterday and this morning messing around with serializing objects from Unity to json, then rendering them in the browser with javascript.

You can access the individual mesh names from the json, and add controls and stuff like you would any other js element on the web.

function onMouseMove(e) {
		mx = e.clientX;
		my = e.clientY;
	}

      camera.rotation.x = (my / window.innerWidth* 2 - 1) * 0.5;
      camera.rotation.y = (mx / window.innerHeight * 2 - 1) * 0.5;

Here's a demo: http://leefromseattle.com/jsonB/page.html

In one word, yes otherwise the answer would be not really.

Take a look at Haxe, OpenFL, Citrus Engine, PlayScript (from Zynga) and then see if you can answer that faithfully.