Impurity importance favours flexible splits

Why might a tree give high impurity-based importance to a continuous noise feature compared with a binary noise feature?

A continuous feature often offers many candidate thresholds, increasing opportunities to find a chance impurity decrease in training. A binary feature has fewer alternatives. Prefer held-out evaluation, permutation or refit-based comparisons, while accounting for correlated predictors and temporal dependence. High training impurity importance does not by itself establish predictive information.