Uhm, hate to break it to you, but they didn't exist until HTML 3.0... and they are just as (and often more) broken cross browser as anything else. Hence the white 'bars' offsetting the bottom borders in opera and webkit that aren't showing up in FF/IE on your current page. (display:block could clear that up)
They also make the markup needlessly complex and take extra time to render.
As to supporting 'the lowest level foundation' I assume you mean old browsers -- and unless you're still catering to netscape 4 users, there's no legitimate reason for it. A properly coded CSS layout will work just fine all the way back to IE 5.5, and if care is taken most of it will work in IE 5.0 -- again, if you're worried about older than that, you're stuck in 1997... and even Win 95 can run IE 5.5, FF 1.0 or Opera 8.5
In an age where many developers are telling IE6 users to hit the bricks. (which I attribute to shortsightedness and laziness)
There's a difference between table based layouts and tables for NOTHING though -- and you've got a nasty case of tables for nothing AND non-semantic markup - which COMPLETELY defeat what you are trying to accomplish! The latter making browsers like lynx and screen readers be effectively useless... much less the rikki fit mobile devices throw on it.
I don't know who told you tables were better for reaching more users -- or that wrapping EVERY SINGLE ELEMENT in a table for no reason was good practice, but they packed you so full of sand you could change your name to Sahara.
ESPECIALLY if you aren't practicing semantic markup. Users of really old browsers or really limited browsers will likely turn CSS off and have their browsers ignore presentational elements like the LONG DEPRECATED font tag and bgcolor attribute.
You're basically practicing 1997 style "for screen only" presentational markup -- the type of markup where people were still using style embeds instead of link and went "media attribute, what's that? WCAG? Never heard of it."
Even worse, the lack of heading tags, lists for menus, paragraphs around the ACTUAL paragraphs (instead of being filled with a IMG and a DIV filled with redundant content?!?) are pretty much flushing your chances of search engines doing anything meaningful with the site... much less screen readers and other accessibility devices having NO way to discern what's what in your content.
Users screens MAY be 1024 wide, but what's that on the side of the screen when maximized? A Scrollbar! Scrollbar and window borders (some OS always show them even when maximized, Some OS like the Mac don't even give you a real maximize) means you have to take about 48px or so off to be on the safe side... On a 1024 wide display maximized your page is going to have a horizontal scrollbar and 40+px chopped off the right side until you scroll.
...which is why a 1024 friendly design should be 976px or narrower, and why a 800 friendly design should be 752px or less...
Though IMHO targeting fixed width in the first place is a steaming pile of /FAIL/... fluid or semi-fluid for the win, and if you're using tables for layout that's EASY.