The big problem was always Accessibility-related semantics. Websites laid out in TABLEs were often quite confusing to screen readers, as TABLE has a lot of supposedly important semantics in how it should be read/engaged with and using a TABLE for layout follows none of them. (What does a table header mean in a layout? Most layouts wouldn't have good headers. How do you describe what a table column is supposed to be for without a column header?) It's a shame that narrative was never clear enough that Accessibility was always the big reason TABLEs were considered a Bad Idea for layout.
(Speaking of downloading a megabyte of data, I recall how long I felt that a 1.44 MB floppy was the best restriction for the size of an entire website. If it was bigger than a floppy you were probably doing something wrong. I stopped counting floppies a long time ago; that person might be ashamed at how many floppies a typical website downloads these days.)