Q: Why not use binary search trees for priority queues?

A:

• Finding the minimum requires traversing down the left branch.
• Adds and removals from binary search trees can be done in O(log(n)) time only if the tree is balanced.
• Binary search trees are not inherently balanced (Example) — Even if they start out balanced they can lose balance after a number of adds and removals.
• In the worst case, adds and removals for binary search trees take O(n) (linear) time.

Binary heaps, when properly implemented, are self-balancing.