https://gateoverflow.in/1245/gate2007-47
you can refer above question and it is clear that comparison require loglog n time.
but that does not mean you can insert element in loglog n time.
we have to shift the element and it require log n time in worst case same as that of heap.
one more thing not related to heap but about binary search and insertion sort
there also you find the position of element in sorted part of array in log n time but you can not improve the worst case time.
it will be O(n^2) only, cause you have to shift the element to its correct position.