Quicksort is superior to Heapsort in practice. Mergesort is the only stable of 3 (in simple variations of vanilla). Thus, it is either quicksort or mergesort, which will be used depending on the situation (in place in memory or external sorting, etc.)
So is there ever a case where the heap data structure is really used for sorting? No matter how much I'm 'Google' or trying to come up with applications, you almost always choose merge / quick sort by heapsort. I never came across a case where a bunch of sorting is really used in my professional life. What would actually be a good use case for heapsort in practice (if at all), out of curiosity?
performance sorting heapsort
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