The only time I use $_REQUEST is when I need to be able to support data from either $_POST or $_GET.
For example, if I have a form that's supposed to modify a record, I might initially pass the record ID in the url as id=X. So when first loading the form, I could use $_GET['id'] to figure out what record we're trying to modify.
However, when submitting the modify operation, the form should be POSTed, since it will be changing data and is not idempotent. In this case, the record ID would be accessible as $_POST['id'] when processing the form submission.
But what happens if there's an error in the form submission and I need to reload the form with a helpful error message? In this case, the form generation code needs to figure out what record to use by looking at the POSTed id, which is not in the URL.
In cases like this, I would use $_REQUEST['id'] in the form display logic, so that it could support either scenario. But for form processing, I would use $_POST['id'] for strict checking.