[Disclaimer: I work at Cliqz]
Although it is anonymous data - currently we are not aware of any de-anonymization attacks - it is still data that came from real persons. We have a responsibility: once the data is out, we have to guarantee that no-one will ever be able to identity a single person in the data. Take also in account that attackers can combine multiple data sets (Background Knowledge Attacks); that even includes data sets that will be published (or leaked) in the future.
You should never be too confident when it comes to security, neither should you underestimate the creativity of attackers. What we can do - and did in the past - is to simulate the scenario in a controlled environment by hiring pen testing companies. If they would find an attack, they will not use that knowledge to harm the persons behind the identities that they could reveal.
That is the main reason. We don't want to end up in a situation as AOL or Netflix when they published their data. By the way, Netflix is an example of a background attack where they needed to combine data sources.
There is also another argument. Skeptics will most likely remain skeptics, as we cannot proof that we did not filter out data before publishing. In other words, there is nothing to gain for us, we can only loose. Trust is important, but for building trust, it is better to be transparent about the data that gets sent on the client. You can verify that part yourself and do not have to rely on trust alone. That is the core idea behind our privacy by design approach.
Those are the arguments that I'm aware of why we will not open the data. However, getting access in controlled environments is possible. If you doing security/privacy research, you can reach out to us. In my opinion, having more people that will try to find flaws in our heuristics is useful. That gives us a chance to fix it before it can be used for attacks.
One notable exception: https://whotracks.me is built from Human Web and all its underlying data can be freely downloaded. We know that it has been already used for research.