Removing “index.php?page=” in .htaccess entirely and once and for all


This question has been driving me nuts. There seem to be hundreds of answers online and on various StackExchange websites, but they either remove index.php (keeping ?page=) like this:

Options +FollowSymLinks -MultiViews RewriteBase / RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule ^(.*)$   index.php?$  1 [L,QSA] RewriteCond %{THE_REQUEST} ^[A-Z]{3,}\s(.*)/index\.php [NC] RewriteRule ^ %1 [R=301,L] 

…or like this:

RewriteBase / RewriteCond %{HTTP:X-Requested-With} !^XMLHttpRequest$   RewriteCond %{THE_REQUEST} ^[^/]*/index\.php [NC] RewriteRule ^index\.php(.*)$   $  1 [R=301,NS,L] RewriteCond %{REQUEST_FILENAME} !-f RewriteCond %{REQUEST_FILENAME} !-d RewriteRule ^(.*)$   index.php/$  1 [QSA,L] 

…or remove both but cause the page to not work (not be recognized as a PHP file), like this:

Options -MultiViews RewriteCond %{THE_REQUEST} ^[A-Z]{3,}\s/+index\.php\?page=([^\s&]+) [NC] RewriteRule ^ /%1? [R=302,L] RewriteCond %{REQUEST_FILENAME} !-d RewriteCond %{REQUEST_FILENAME} !-f RewriteRule ^([^/]+)/?$   index.php?page=$  1 [L,QSA] 

How the heck do I remove index.php?page= and still get the remaining file/URL to be recognized as a proper PHP file?