The SiteIcon uploader in SpaceSettings suggests that the file to be uploaded be a small image but it will happily accept:
Either of these result in undesirable behavior.
This is already done with the drag and drop version recently done by @colmjude. It appears there's no easy way to access the file's type if we want to continue to have the form just be a form. We haven't actually had a bunch of problems with this, so will leave it lie.