Application letter with high confidentiality notice is not quite strange to headhunters.
The truth is that most senior level candidates always want to keep their job search confidential and maintain it until shortlisted. The unwillingness to share about their job searching is included but not limited to their personal information (even their name and their current company). This attitude tends to be common in both junior and mid-level as well.
Clearly, if you agree to be candidate, you put yourself at risk with your current company. Or if you pursue a career in a specialized industry/field, moving to other company in the same industry, especially competitors, shouldn’t be public during hiring process.
Therefore, should headhunting industry make a change? “Keep candidates information confidential” with client until shortlisted and client should be responsible for saving information of these candidates during hiring process.
I’d be very interested to your opinion.