I think this would be nice to have! Though only would need to change the current css rather than overriding all images. Currently markdown images have a light grey border and a tiiiny margin:

.typography--md img {
    display: inline-block;
    max-width: 100%;
    margin: .125rem;            /* Tiny margin */
    border: 1px solid #515157;  /* Grey border */
}

I don't believe the border property is necessary since it presents issues with transparent images, as Kitsune said.

Also found that the added margin causes the right-hand border to disappear with images on the profile page, which can look odd:

It would be nice to at least have the disappearing border fixed, though it'd be nicer to have no border at all :)