Considering that I've developed a screen reader from the ground up, worked on the Narrator screen reader shipped with Windows, and routinely used screen readers to browse the web for almost 20 years, I think I know a thing or two about this.

So, it's true that screen readers have heuristics for detecting layout tables. But those heuristics aren't perfect. They're not even that sophisticated, at least the ones that I worked on. And some (most?) screen readers automatically announce any table that they don't detect as a layout table, even when continuously reading straight through the document. Notably, the screen reader I developed myself, which was the first one I routinely used, doesn't automatically announce tables unless the user is manually moving through the page, because I wanted to minimize verbal clutter when casually browsing the web. But when I went to work at Microsoft and started using Narrator to read my work email, I found the tables in certain HTML emails very annoying. Granted, Narrator didn't yet have a layout table heuristic at that time, but even when it did, that didn't entirely solve the problem. Luckily, there was also an overhaul in Narrator's verbosity levels while I was there, and that allowed me to eliminate the clutter of layout tables by reducing the verbosity level in my personal Narrator settings, perhaps at the cost of missing some other things.

Nested divs per se aren't a problem. Implementing a widget as a div without the appropriate ARIA markup is a problem.

This feels inline with what I intended. Used sparingly, tables probably weren't that atrocious to figure out. Similarly, deliberate use of semantic tags is likely better. I question if things are deliberate are much better now. But, you provide a convincing and authoritative answer there.

Html email feels like a trap. They are about turning up the volume and getting returns. Not about being accessible. Is that not the case?

About HTML email, I think it's different in a work context. When I was at Microsoft, some official messages, that were actually important to read, were laid out in the style of an HTML marketing email, complete with heavy abuse of layout tables. Ditto for automated notifications, e.g. about bugs or PRs.

Ah, that makes sense. And feels like a mistake from the department that sent the messages.

My gut is still that better tooling support for standard messages would have helped faster than more primitives in the message. But, I welcome evidence that I'm wrong.

It really depends. If table cell order happens to conform with a logical reading order, yeah, screen readers generally figured out when to ignore table semantics. But if the reading order does not make sense going row by row, then they are terribly broken.

Nested divs aren't that bad. (Ignoring overall performance considerations. And even then I'd suspect that's less a concern than download and running all these JS libraries.) Nested divs with a mish-mash of poorly applied ARIA can get pretty bad though!

Table layouts are also terrible for anyone who is not viewing the site at the browser width you designed it for. Accessibility is more than screen readers, and the ability to zoom or adjust browser width or display on a different device (hello mobile) is incredibly valuable for a lot of people. And I'd argue that the "ease" of using table layouts disappears as soon as you try to accommodate for any of that.

Right, my complaint in nested divs is more when they are a giant mix of different levels with no real discernable logic at the markup level. I think my memory is more from the garbage we made in early 2000s, though. I haven't tried to look at any modern page markup lately.