I know decision trees commonly reuse continuous features down a particular branch of the tree and splitting them in different locations. I am wondering what the downsides are to disallowing this?
For context, I am attempting to use a binary classification decision tree to create a white-box model of a feature hierarchy. Top node would then be the feature that gives you the most information gain about the binary classification. This will also establish a context, basically which feature will give us the next highest information gain conditioned on our current path.
In this hierarchy, reusing features seems like it would disrupt the actual hierarchy which is why I want to disallow reuse of features.