Increase-key and decrease-key in a binary min-heap
The reason that your operation is not listed, is that one is not simply interested in all operations that can be easily implemented using a certain data structure, but rather the other way. Given a set of operations, what is the most efficient way (in terms of space and time) to implement these operations. (But I add more to this later)

Binary heaps implement the abstract data structure priority queue, which asks for operations is_empty, add_element (a key with its priority), find_min, and delete_min. More advanced queues also allow one to decrease the priority of the key (in a min_heap) or even increase it. In fact, you have given an implementation.

Two remarks. Your operation is used in the heapify function, that efficiently constructs a heap from an array. In heapify your operation is repeated (starting from the last key).

Then, most importantly, your code uses the position of the node. For the pure data structure priority queue that is cheating. That data structure asks to perform a certain operation given a key. So in order to decrease or increase the priority of an element, you will first have to locate it. I think that is the main reason it is not listed.