Tables in web design are a thing of the past. They are not used anymore.
Back in CS3 (and maybe a couple versions after that) you could configure the output HTML. You can't do that anymore. The only way to get the HTML at all is to copy it from that browser preview. The HTML that Illustrator generates has been deprecated for years, so they just abandoned doing it at all and you are basically stuck with the most modern HTML code it was ever capable of.