Since you can rewrite anything to "look" static, there is no point in doing just for the file extension since search engines know this and don't give one an advantage over the other. However if you want to add keywords to the URL, that could have some small benefit to you. Or if your URL is very long or packed with query parameters, it may also help from the human perspective.
I would argue that the file extension stops the bot from making up more versions of the URL. http://www.example.com/example bot spin: http://www.example.com/example/ http://www.example.com/example/index.php
index.php (or asp) becomes the page for everything