index.php is shown whenever wordpress doesn’t find an appropriate page template. Generally people use it as the template for their site’s blog. If you are absolutely sure that it will never be reached, you can leave it empty. Just make sure you have that file present, otherwise the theme will not work
As a personal preference, when coming across this kind of situation, i just rename one of archive.php or home.php to index.php which will work just as well for almost all of the situations