In my company I've been noticing some binary classification modeling code that replaces bins of a continuous variable with the corresponding Weight of Evidence (WoE) of the given bin. As far as I understand, WoE for some bin $B_i$ of some variable $X_j$ is calculated by
$$\text{WoE}_{ij} = \ln(\frac{P(X_j \in B_i | Y=1)}{P(X_j \in B_i | Y=0)})$$
where $y=1$ is the positive target and $y=0$ is the negative target of a binary classification problem.
I understand the use case of WoE to help turn a continuous variable to a categorical variable by determining reasonable binning boundaries. What I don't understand is the use case of replacing these bins with the WoE scores themselves.
Doesn't this approach introduce data leakage? Specifically, isn't it problematic that this approach uses $Y$ to transform $X$, which is subsequently used to predict $Y$? In other words, it seems to me that information from $Y$ is indirectly being used to predict itself, but maybe I'm missing something.
This question ostensibly discusses this problem, but OP is mainly concerned with the interpretability of $X$ when taking this kind of approach. I can't find any discussion of data leakage.
