Yes, this is how it should be done. Actually, if I ran a company, I would go further. There would be no affirmative action or quota nonsense. Best person for the job, that is all. I care only about ability, work ethic, and whether they are a fit for the team/company. Anyone whose resume was being forwarded would have the name and any other gender/age/race info removed by HR before sending. And for anyone who came in for an interview but we passed on I would require the written, documented reason just to have for record-keeping. That way, HR could periodically go in and retroactively analyze to see if there was any sort of bias (intentional or not) or other funny business going on.

That's how you maximize your productivity and efficiency and, by extension, profit. It also motivates people because they know they are much closer to a true meritocracy.