As this article points out, organisational culture is a delicate balance between many things, including accountability and anonymity:

Though some assurance of anonymity is necessary in a few sensitive and exceptional scenarios, dependence on anonymous feedback channels within an organization may stunt the normalization of a culture that encourages diversity and community.
Anonymity can be helpful and positive:
For example, an anonymous suggestion program to garner ideas from members or employees in an organization may strengthen inclusivity and enhance the diversity of suggestions the organization receives. It would also make for a more meritocratic decision-making process, as anonymity would ensure that the quality of the articulated idea, rather than the rank and reputation of the articulator, is what's under evaluation. Allowing members to anonymously vote for anonymously-submitted ideas would help curb the influence of office politics in decisions affecting the organization's growth.
...but also problematic:
Reliance on anonymous speech for serious organizational decision-making may also contribute to complacency in an organizational culture that falls short of openness. Outlets for anonymous speech may be as similar to open as crowdsourcing is—or rather, is not. Like efforts to crowdsource creative ideas, anonymous suggestion programs may create an organizational environment in which diverse perspectives are only valued when an organization's leaders find it convenient to take advantage of members' ideas.
The author gives some advice to leaders under five sub-headings:
  1. Availability of additional communication mechanisms
  2. Failure of other communication avenues
  3. Consequences of anonymity
  4. Designing the anonymous communication channel
  5. Long-term considerations
There's some great advice in here, and I'll certainly be reflecting on it with the organisations of which I'm part.

Source: opensource.com