I have successfully implemented a blind hiring process with a client, a PE-backed RegTech firm. Benefits include reducing unconscious bias in the hiring process. In a competitive market like RegTech this allows more talent in to the top of the funnel with the client. Challenges are largely administrative - if you are managing multiple candidates referring to the as C1, C2 etc as opposed to by their names means you have to double check who the candidates are a lot.
We have on request instituted a blind hiring process for a client who was trying to reduce unconscious bias. While the theory has potential, there is a major flaw as it simply "kicks the can" down the road. If there is potential bias at the CV vetting stage, there is a high chance this may manifest during interviews anyway.