This only works when there's only one site hosted at 10.0.0.1. When an HTTP request is made, it looks like this (not trying to be pedantic here, I'm sure you know how HTTP requests are made):
GET /picture.jpg HTTP/1.1
Host: host.sample.com
[Other header: value]...
Many times, the Host header is an essential part of the equation. If, for instance, you have a single IP serving as an endpoint to many different sites, you need the Host header to decide where you'll look for the resource "picture.jpg".That could of course be solved with something like
<img src="hxxp://host.sample.com/picture.jpg" ip="10.0.0.1">
or even
<img src="hxxp://10.0.0.1/picture.jpg" host="host.sample.com">