It’s best practice to always use prepare but the main use of it is to prevent against SQL injection attacks, and since there is no input from the users/visitors or they can’t effect the query then that is not an issue in your current example.
But like I said before it’s best practice to use it and once you start using it you never stop, so in your example you can use it like so:
$tablename = $wpdb->prefix . "my_custom_table";
$sql = $wpdb->prepare( "SELECT * FROM %s ORDER BY date_created DESC",$tablename );
$results = $wpdb->get_results( $sql , ARRAY_A );
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