Is sharpening an image (RAW) useful?

Let me start by saying that I am older, and so maybe it is just my age catching up with me. Still, I'd like to know from young and old alike, if I am missing something.

What I might be missing is the real use of sharpening. I do sharpen my images by some obligatory amount as part of my workflow, but for the life of me I could not tell you at first glance, or really even second glance, which of my photos I have sharpened. I am referring to RAW files btw, since I know JPEG is often pre-sharpened. I will load a photo into Lightroom, and increase sharpness by some amount and look at the photo and blow me down if there is any difference. I can only assume that others notice it more readily than I do because otherwise we would not have the sharpen slider!

Now, if I dragged that sharpness all the way, then yes I notice the terrible jaggedness introduced by the sharpening, but who wants that? I was once told that you should only sharpen in great moderation, and if you can notice the effect of sharpening, then you've gone too far already. Great advice, but if you aren't going to notice it, why bother?

And also, I will admit that if I zoom in to 300%, I can see some subtle effects of sharpening, but that is all.

Other than new glasses, what should I be looking out for in sharpening photos, and when is it necessary (i.e. do you sharpen sometimes, when the image is soft, or all the time to every photo)? Is (proper) sharpening obvious to you as a viewer (not photographer)?