Why couldn't you use a cashier's check?
A cashier's check is like a domestic SWIFT.
It's difficult to imagine in a modern world, people or institutions writing or printing something on a piece of paper, and saying, "here, this is money".
Got stuck behind someone at the Carrefour (grocery store) paying with one. Ugh.
Some people/business will still ask for a cashier's check though.
I agree, cashiers checks are safer, but some people have reasons to prefer cash.
In the UK, government benefits are paid by bank transfer.