Wouldn’t it be great if you can specify different styles per page all from the stylesheet? For example, your home page may have a larger header section than the rest of your pages. The solution would be to add a different class on each page so you can do something like this.
Cross-browser compatibility can be a major pain. The philosophy for most web developers is to code against a standard-complaint browser (Chrome), then apply CSS hacks later for other browsers that need to play catch up (Internet Explorer). In other words, it is better to make your code forward-compatible and apply backward-compatible hacks instead of the other way around.