They are held responsible to a certain point yes, and shipping services actively control high-risk shipments (up to the point they check the box contents, for airplane shipping, for batteries for example).
It's forbidden to send money through mail in many places.
When you go to the post office to send money, the post office verifies your identity, the payment method, the sanctions list, etc and keeps the records for the authorities.
If you decide to violate the rules and send cash in a letter, the postal service allows the authorities to access the raw packages and full information, and full access to it, whether to use cash sniffing dogs (they really exist), etc.
Also, a fundamental difference with crypto exchanges:
Whether you send large amount of cash for criminal activity via the postal service or whether you send a large amount of books the postal service isn't going to benefit more, so they don't have to encourage criminal activity.
It's forbidden to send money through mail in many places. When you go to the post office to send money, the post office verifies your identity, the payment method, the sanctions list, etc and keeps the records for the authorities.
If you decide to violate the rules and send cash in a letter, the postal service allows the authorities to access the raw packages and full information, and full access to it, whether to use cash sniffing dogs (they really exist), etc.
Also, a fundamental difference with crypto exchanges:
Whether you send large amount of cash for criminal activity via the postal service or whether you send a large amount of books the postal service isn't going to benefit more, so they don't have to encourage criminal activity.