I personally am not a fan of anything anonymous other than ethics hotlines.
Its hard to follow up and get more detail to fix/improve something if you can not identify the source.
Also, as you can see on the internet, anonymity often brings out the worst in people--making them feel like they have agency to badmouth and belittle.
If you are planning on using anonymity because your organization has a trust issue, I would work on improving that before you launched a survey
Well, it depends on what is done with the survey results. Does the company share the results or does it stay in the HR department with specific items tagged and associated with specific managers, or does it point to a suggestion to modify the entire culture of the company.
I believe the surveys are a great communications vehicle, but require communications of results in return for participation. It is likely that more people in an organization might feel like one of the comments and feel that the collective company understands their views.
If it is merely used as a morale survey it will not generally produce an unbiased response. My experience with using surveys internally is that there are the whiners and complainers looking for an outlet, and the minority of responses is positive or neutral. Nonetheless, I am in favor of them.
Generally I'd say neutral to bad i.e. I've rarely seen them change much that is useful. Although culture is a generic term across an organisation, most people's engagement is really mitigated by the local climate in their team, heavily influenced by their manager. That's where engagement happens - not in terms of generic scores on the things around the work, but in the work itself. And the surveys don't survey that.
Regarding the future of business coaching, I choose to believe it is and will continue to be necessary for companies to avail themselves of outside coaching expertise and programs the focus on the true nature of coaching which is self-improvement that improves every employee's view of their work and how they can succeed. Coaching should be a part of any organization that has a customer facing sales organization, and a customer facing service organization. It works, it helps people to assess their need to improve and how to achieve it, and pays great dividends to companies that support it at all levels of management. In truth, perhaps every level of an organization can benefit from some model of basic coaching if nothing more than self-awareness of how an individual can be better if they choose to.