Well, for one thing, $_POST is a superglobal, so you can use it in functions directly. With your method, you'd have to use $GLOBALS or add a "global $varname" line. So it can save you a little typing.
Also, with $_POST, you have no possibility of unexpected input clobbering other variables and so forth. With import_request_variables(), you have the potential for the same kind of scenarios that cause problems with register_globals. Of course, you can avoid that by coding carefully, but it's just one more thing to worry about.
There are also a number of situations where using superglobals is just more convenient. For example, you sometimes need to loop over the POST data, which is more convenient when it's already in an array. Likewise, if you want a central routine to sanitize input, it's a bit easier with superglobals. It's also more straight-forward to use superglobals when you have data in the GET, POST, and cookie variables, as it's clearer where the data's coming from and you don't have to worry about having the same name in, e.g. GET and POST.
So yes, there are some advantages to using superglobals. I would definitely recommend using them.