In ML, we often talk about the bias-variance tradeoff, and how increasing model complexity both reduces bias and increases variance. I understand why increasing model complexity reduces bias at first, but it's less clear to me once you get into overfitting territory.

Here is the formula for the bias: $\operatorname{Bias}_D\big[\hat{f}(x;D)\big] = \operatorname{E}_D\big[\hat{f}(x;D)- f(x)\big]$. As you increase model complexity past a certain point (ignoring double descent), the model starts to heavily overfit its training data, and starts to make wild, increasingly incorrect predictions on much of the rest of the data distribution. Why would this reduce the bias on the entire data distribution?

In this post: Does bias eventually increase with model complexity?, the accepted answer claims that the average of the model's predictions across training sets sampled from the data distribution will average to something close to the true values. But it's not clear to me why this is true, and why it can't average to something else.