So he was 90 years old when he wrote that. That is really cool, especially in the context of this section of the obituary:
> In many respects, Fano was one of the world’s first open-source advocates. He frequently described computing as a public utility that, like water or electricity, should be accessible to all. His writings in the 1960s often discussed computing’s place in society, and predated today’s debates about the ethical implications of technology.
> “One must consider the security of a system that may hold in its mass memory detailed information on individuals and organizations,” he wrote in a 1966 paper he co-authored with Corbató. “How will access to the utility be controlled? Who will regulate its use?”
There is significant research effort these days on going beyond unbiasedness and asymptotics, which in many cases has been beaten to death and is "classical", though there are still plenty of questions.
Here is a simple illustration of unbiasedness/going beyond it. Consider n iid (independent and identically distributed) coin flips of coin of P(heads) = p, and based on the observations, we want to estimate p, call the estimate p'. Optimum estimate in the sense of minimax - min (over estimators) max (over p in [0, 1]) E[(p-p')^2] is not the simple maximum likelihood which is the sample average. Sample average yields a score of (1/4)(1/n), while optimum is (1/4)(1/(sqrt(n)+1)^2), which is slightly lower. It is natural to wonder why people care, typically the motivation is in high dim statistics where there is dependence on the dimension as well. In such a case fine grained characterization of performance sometimes affects the scaling in terms of the target loss amount and dimension, i.e the asymptotics now has at least 2 parameters, sometimes more.
My personal unhappiness with these problem formulations is their lack of robustness to transformations - suppose I now want to estimate p^3 instead of p, the optimum min-max will change in most cases, and definitely does here. Plugging in the sample average and then cubing is far more intuitive, and often works fine even though it is not optimal. There are more extreme examples of this, but that will take the thread too far afield.
If one is interested in the topic of biased estimators, I suggest reading about James-Stein estimators and more generally shrinkage estimators.