Is that a real problem for professional users or just a kluge to work around the ever-decreasing IT skills of today's generation that can no longer do basic things such as window management?

I think an OS-managed popup window is superior to a page-managed modal since it allows you to move the window out of the way or even switch away from it, where as a page-managed modal is generally fixed in place, blanks out the parent page, and the only way to get back that parent page would be to dismiss the modal which discards your input.

I'm also not sure whether the accessibility concerns are substantiated - surely window management would be a well-trodden path for any screen-reader user and whatever you build yourself in-browser would have different and unexpected semantics that would require the user to get used to it.

From the link you posted:

    The HTML <dialog> element is used to create both modal and non-modal dialog boxes. Modal dialog boxes interrupt interaction with the rest of the page being inert, while non-modal dialog boxes allow interaction with the rest of the page.

The modal dialogs are easier for the programmer to use but they're quite inconvenient because generally, they ask you a question you can answer only by looking at/interacting with the rest of the page. Which you can't do (the modal dialogs on web also almost never can be dragged around).

The term "modal" pre-dates <dialog> by a huge amount, and generally refers to a popup within the same window that prevents interacting with what's behind the popup (I believe the term comes from how you "change modes" when it appears). On the web they used to be implemented using <div> and CSS, often with some sort of javascript library so you didn't have to do it yourself.