Significance of Number of Calls and Reset Call in Ball Tree
Indeed, they don't seem to be used for anything.  Probably they were included for some initial debugging?
An issue (and a linked PR) discussing these methods:
https://github.com/scikit-learn/scikit-learn/issues/13330
(At time of posting,) searching for n_calls only finds results in _binary_tree.pxi, and none of them seem actually used for anything other than tracking the number of distances computed:
https://github.com/scikit-learn/scikit-learn/search?q=n_calls