Using your method it would be possible, however it would be a fairly elaborate process. I can change the entire layout of the site by just editing no more than three or four lines of the stylesheet. It's a very straightforward process. When you use tables you basically lock the design in place, and to dramatically change the layout you'd have to re-arrange things quite a bit. Also, when stylesheets are used, the client has a lot more control over the design as well. Which may not seem important on the surface, however as web access starts becoming available on more devices (e.g. cell phones, PDAs, watches, etc) the usefulness starts to show through. This is actually one of the main purposes for CSS, though I like to use it for other reasons (e.g. simplicity). A cell phone, say, can take a site that has a pure CSS layout and ignore the stylesheets and just download the data contained on the site, and from there format it in the best way for a 2x2inch screen

. I am not aware of any mainstream devices that take advantage of this currently, however as CSS becomes more prevalent you'll start to see devices taking advantage of this. A good example of a mainstream site is wired.com, that is a completely table-free pure CSS layout.
http://www.meyerweb.com/eric/css/edge/ has some good info.