Why is client-side web still using an interpreted language?

To my knowledge JavaScript is the only language that will execute on the client side after the HTML file has been retrieved from the server. As far as I know JavaScript is by no means compiled in anyway and thus it is an interpreted language.

With Web becoming more and more popular, so much so that some say mobile and desktop applications will soon cease to exist.

We see new technologies like WebGL, that makes use of JS.

When I develop for WebGL I have to optimize so much more to achieve a reasonable performance benchmark, then what I would have to for PC or Console.

So why do we still use an interpreted client side language? Is it a security issue, hardware (cross platform) issue or is it simply because it's difficult to introduce such a large change into the web architecture? I know web developers have headaches over even the smallest and simplest changes, like using CSS 3, simply because not everyone has their browser up to date.

Am I correct in thinking that interperated languages are slower then compiled ones? Am I making sense or are my assumptions completely incorrect? I am by no means a JS/web expert, please educate me.