What is the advantage of using home.php over index.php for the front page

If you look here [is_home vs is_front_page] you’ll see that is_front_page() is true regardless of what the homepage is set to in the WordPress settings. This means that if you don’t plan on releasing this publicly (i.e. short-run usage) then just having a front-page.php should suffice. is_home() is set based on your blogs page (which may or may not be the homepage, depending on whats set in WordPress Settings)

Also, here’s a link to the hierarchy of which templates are chosen under what conditions: Template Hierarchy