Why doesn't inset box-shadow work over images?

Because the shadow is part of the parent container it renders below the image. One alternative is to have a div which places a shadow overtop the image like so:

<main>
    <img src="https://upload.wikimedia.org/wikipedia/commons/d/d2/Solid_white.png" />
    <div class="shadow"></div>
</main>

CSS:

.shadow {
    position: absolute;
    width: 100%;
    height: 100%;
    box-shadow: inset 3px 3px 10px 0 #000000;
    border-radius: 20px;
    top: 0;
    left: 0;
}

Edit: I've updated the fiddle to include border radius on the shadow and on the img which solves the issue identified in the comments.

https://jsfiddle.net/WymFE/3/

Just to chime in on this, because I was just creating something similar...

I hate polluting my markup with extra elements for the sake of styling, so the CSS solution is to use the :after pseudo element:

main::after
{
 box-shadow: inset 3px 3px 10px 0 #000000;
 content: '';
 display: block;
 height: 100%;
 position: absolute;
 top: 0;
 width: 100%;
}

It's probably too late for what you were trying to do, but is the better solution in my estimation.

The reason it's not overlapping is because the image is inside the div, so the image is on top of it. The image is higher (closer to the user) than the div.

You can change the image to use position: relative; z-index: -1, and have the containing div use a border instead of setting background color on the body. You'll need to use box-sizing: border-box to include the border in the width of the div.

DEMO

body {
    background-color: #FFF;
}

main {
    position: absolute;
    bottom: 0;
    right: 0;
    width: 100%;
    height: 100%;
    border: 60px solid black;
    box-shadow: inset 3px 3px 10px 0 #000000;
    box-sizing: border-box;
}

img {
    z-index:-1;
    position: relative;
}