Page "Public-key cryptography" Paragraph 30

The critical advantage in an asymmetric key system is that Bob and Alice never need to send a copy of their keys to each other.

This prevents a third party-perhaps, in this example, a corrupt postal worker-from copying a key while it is in transit, allowing the third party to spy on all future messages sent between Alice and Bob.

So, in the public key scenario, Alice and Bob need not trust the postal service as much.

In addition, if Bob were careless and allowed someone else to copy his key, Alice's messages to Bob would be compromised, but Alice's messages to other people would remain secret, since the other people would be providing different padlocks for Alice to use.