Well REST allows for resources to be accessed as they are: resources. Using POST/GET query parameters implies that the server should do some actual processing on these to deliver the requested resource. With REST, you can have the resource be a static file on the server, no processing required.
I don't think you need REST to access a static file.
HTTP is a -- the prototypical -- RESTful system, and its not exactly uncommon for accessing static files on the web.
REST isn't just special-purpose APIs built on top of HTTP (nor, for that matter, does it require that an API be built on top of HTTP at all.)