People have been using HTML tags non-semantically for a very long time and, to be honest, before HTML 4 you often didn't have a lot of choice in the matter.
Still, when I was getting back into web development in 2013 I became aware of an "I can just use <div> and <a> for everything, and then stick Bootstrap classes and event handlers on to get it to look and behave the way I want" attitude that had become pervasive amongst developers.
Now, to be fair, at the time this was legitimate: in 2013 older versions of Internet Explorer were still quite prevalent. They didn't support newer HTML5 constructs, or proper styling of certain elements. The <div>/<a> approach was often the only way to get things to look good, or even to look the same, across all browsers.
Those days are long since gone (for most of us, anyway), but I wonder if the reason we continue to see this style of HTML is that we're still living in a sort of post-IE hangover period? Old habits die hard.
 I'm aware that even now not everybody has the luxury of pretending that IE doesn't, and never did, exist.
 Again, reminds me of the migration from earlier versions of HTML, where you'd really had to do things like use tables for layout and use various HTML elements for styling (with variable cross-browser support), to HTML 4, where you nominally didn't (except, of course, that not all browsers were created equal).
This is begging the question! You start with the assumption that assistive technologies can handle table-based layouts well, and then work backwards from the conclusion that you’re trying to prove.
It may shock or surprise you, then, to learn that in actual fact, table-based layouts caused problems for screen readers (and still do, if I am not mistaken). There are a number of other ways that websites break screen readers, and the difference today is that (1) table-based layouts are hardly necessary or even popular these days and (2) more people are suing over ADA violations for inaccessible web pages.
The screen-reader tools do not fully rely on HTML semantics, but they do need some logic to differentiate between tabular content and purely presentational <table>. The reason for this should be fairly obvious once you look at any actual web page—when you navigate tables, you want to go by columns and rows, but if you are reading a table used for layout, you probably just want to flatten it and go through the entire thing in linear order (more or less). The process can be disorienting for people with screen readers if your site is poorly designed.
Of course, if you just make assumptions and guess about how screen readers and assistive technologies work, there is a good chance that your guesses are wrong.
IMO, it's more about developers just using Bootstrap without reading the documentation. The examples are pretty well done, they use semantic elements and are accessible.
For example, the Navbar element has a good HTML structure and uses `aria-label`s that announces what's going on to assistive technologies.
Another one is the modal example, it has semantic elements, the `tabindex="-1"` attribute to make it accessible to keyboards and the correct use of the `aria-label` as well.
So, their documentation pretty much teaches you how to use it correctly. I'm not a fan of Bootstrap myself, but I think throwing the blame at it is unfair.
Good to see they improved, i guess :-)
(I probably paid a lot more attention in 3.x documentation than most because of the mistake in a past life of forking Bootstrap 3 for an enterprise project and trying to keep it in sync with upstream. Never again would I consider doing that.)