Very interesting, especially when compared to shogi (Japanese chess), where captured pieces can be dropped in anywhere on the board. So for shogi players this "ideal square" calculation can be even more natural and more flexible as well: besides the "getting existing pieces from A to B", the "drop on B" is a lot simpler. No wonder that piece exchanges (so there is something in the hand to drop) are basic feature of the gameplay.

(Source: being a fan of shogi but very very very early in my learning journey, so experts would likely describe this differently.)