Why is a cash advance done using a credit card so much more expensive
than a purchase with a credit card, or withdrawing cash from an ABM?

The cash advance is so much more expensive because the credit card
assumes that it will probably be an emergency when you want to use it,
and therefore you won't care about the 30% interest rate. It's the
same reason those "paycheck cashing" places are so expensive.

Credit cards are free from usury laws, too, so they can charge
whatever skyhigh rates they want.