"I know that a lot of people paint contracts as being evil - but please note that in some states dance studios are required by law to have written contracts."
Usually this requirement only comes into effect when prepayment is involved.
Most serious dance teachers do not require prepayment. You pay for each lesson after that lesson, and get the best rate that they offer when you do so. They have no more interest in incurring future obligations than their students do.
However, even in a jurisdiction where a "contract" is required under all circumstances or if the studio/teacher wants prepayment, a boilerplate contract for a single lesson would still be permissible. It could double as a receipt.
"Packages" are entirely an invention of the studio owners, and are all about business, not about dancing.