The real problem is if you need min/max at the same time. Then you not only need a min heap and max heap, you also need to track what was already popped from either heap! This is because in python you can't delete an element if it's not at the root. So tracking "tombstones" will let you pop from one heap, then know to ignore it the next time it comes up in the other heap.
This is of course super complicated to maintain and I get it wrong all the time. Luckily only shows up in algo interview problems.
