1. The div is not keyboard-focusable by default, so you need to add `tabindex="0"`.
2. By default, the div does not trigger click on Enter/Space, so you need to add a keyup handler to make it do so.
3. Screen readers won't report the div as a button because they can't identify widgets based on how they look, so add `role="button"` as per the ARIA spec (only on first cup of coffee now, so I'm not providing a link.)
Yes, it isn't super complicated, but a) most don't do it because they look identical and b) multiply that by any other widget where the HTML version is replaced with a div and suddenly things get complicated. If you're not a keyboard user, you may not understand how the web works without a mouse. All that is lost when switching to divs.
This says nothing about how OS/screen reader combinations differ in key handling, nor about how complex widgets such as multiselects include similarly complex key handling. Also, the above ARIA is super simplistic. It doesn't handle situations where, for instance, you have multiple roles and have to toggle some of them based on what item is selected, what item is focused, etc.
So, TLDR: It's so much better to use the HTML elements specifically designed for a certain task because you get a lot for free that is taken for granted. That said, I like how Semantic specifies how my UI might look, an wish I could have the best of both worlds.