From my point of view, this is a serious lack. Knowledge of the distribution of the hash rate is crucial. This invalidates one of the principles of blockchain: don't trust, verify. How is it possible to know whether mining is controlled by finance or government?
That's a valid point but there is no provable ways to accurately tell where the hashrates are, what the hashrate is or the distribution of it. Bitcoin is designed to be transparent, but unfortunately the pseudonymous nature also means that it is difficult to ascertain certain things beyond a reasonable degree. I don't think it is easy to do so, or if you have a feasible idea to do it, then we can hear from you as well. If not, then I believe that should be the end of that discussion.
POW or basically any mechanism favours those with the most resources, because it functions by game theory and the assumption that you stand to lose the most if you are dishonest.