I'm absolutely an advocate for corners that are rounded to a reasonable degree. As you stated, perfectly sharp corners can produce a harsh, inorganic aesthetic that can be distracting to users.

Even very round corners can be contextually appropriate.

There's a world of difference between a few pixels of roundness, and making your entire website look like a fisher-price toy.

Round, organic designs can be complex and visually pleasing. They take a lot of work to execute well, and are rarely confined to the simple rectangles that dominate modern interface design.

The large border radius on modern UIs doesn't contribute anything interesting to previous UX other than the novelty of round corners. It hasn't been motivated, or motivated any meaningful new design approaches. All it's accomplished is that it's turned UI elements into rectangular pills that function almost exactly as they did before.

I see it as an aesthetic reflection of the modern technologist's attitude towards their user-bases.

Edit:some grammar