Why isn’t object-fit working in flexbox?

From the specification:

The object-fit property specifies how the contents of a replaced
element should be fitted to the box established by its used height and
width.

The key term being: fitted to the box established by its used height and width

The image gets replaced, not its container. And the box established by its used height and width relates to the image itself, not its container.

So, scrap the container and make the images themselves the flex items.

.container {
  display: flex;
  flex-direction: row;
  width: 100%;
}

img {
  object-fit: cover;
  flex: 1;
  margin-right: 1rem;
  overflow: hidden;
  height: 400px;
}

<div class="container">
  <img src="http://placehold.it/1920x1080">
  <img src="http://placehold.it/1920x1080">
  <img src="http://placehold.it/1920x1080">
  <img src="http://placehold.it/1920x1080">
</div>

Revised Codepen

Additional Details

5.5. Sizing Objects: the object-fit
property

The object-fit property specifies how the contents of a replaced
element should be fitted to the box established by its used height and
width.

Here are three of the values:

• cover

  The replaced content is sized to maintain its aspect ratio while
  filling the element’s entire content box.

• contain

  The replaced content is sized to maintain its aspect ratio while
  fitting within the element’s content box.

• fill

  The replaced content is sized to fill the element’s content box.

With cover the image retains its aspect ratio and covers all available space. With this option, much of an image may be cropped off-screen.

With contain the aspect ratio is also maintained, but the image scales to fit within the box. This may result in whitespace on the left and/or right (portrait fit), or top and/or bottom (landscape fit). The object-position property can be used to shift the image within its box.

With fill the aspect ratio is abandoned and the image is sized to fit the box.

Browser Compatibility

As of this writing, object-fit is not supported by Internet Explorer. For a workaround see:

• Neat trick for CSS object-fit fallback on Edge (and other browsers)
• fitie – An object-fit polyfill for Internet Explorer
• object-fit-images – Adds support for object-fit on IE9, IE10, IE11, Edge and other old browsers
• Polyfill (mostly IE) for CSS object-fit property to fill-in/fit-in images into containers.