HTML and JavaScript are essentially plain text - the approach of rendering this code in browsers then using other tools to check cross-browser compatibility, security, accessibility and performance is wasteful and counter-productive.
Non-functional issues arise from the code - an image of a dog in IE will not render as a cat in Firefox. White-space in the source between an img and a div will always appear in IE6 and never in FF.
Computers are very good at checking text against a set of rules and very poor at interpreting images. Asking a developer to read through his own code and then using an automated tool to check the output forces both humans and computers to do the very tasks they are worst at. Static analysis based on rules submitted from developer/tester/user experience reverses this situation.