This is an interesting approach. We will probably try it in the future but at the moment feedback says that candidates almost always want more information (more about the company, more about the people they'd be working with, more about the kind of work they'd be doing). But I definitely agree on how it might take the stress out of the process.

The only issue is that hiring and getting hired requires significant commitment on both ends and long term anonymity might not work really well under those conditions.