Red Black Tree clarification
If you check the proof height-balancedness of red-black trees, you'll see that we essentially analyse the black-height $h_b$ of the tree which, by another important invariant, is the number of black nodes from the root to any leaf.

The property you cite then gives us the right half of

$\qquad\displaystyle h_b(T) \leq h(T) \leq 2h_b(T)$,

which allows us to carry over bounds on black-height to usual height.