What you say is extremely wrong and this misconception is very dangerous.
When an authenticated connection between a client and a server (or any other 2 computers) is established, before the connection can be initiated both ends must already have a piece of information that has been copied to them through a secure channel, otherwise the authentication is impossible.
The 2 pieces of information may allow direct reciprocal authentication, i.e. the client may have the server certificate and the server may have the client certificate.
It is also possible to have indirect authentication, e.g. the server sends the server certificate to the client and the client sends the client certificate to the server during the initiation of the connection.
However, for indirect authentication, both the client and the server must had been previously paired with a server hosting the certification authority.
This means that the root certificate of the CA must have been transferred through secure channels to the client and to the server, and also that the client certificate and the server certificate must have been transferred through secure channels to the CA for signing and then back to the client and the server.
So setting up the computers for indirect authentication through certificates requires significantly more transfers through secure channels than setting them up for direct authentication.
The advantage of indirect authentication appears in an organization with a great number of computers, where indirect authentication reduces the number of secure pairings that must be done from N*(N-1)/2 to N.
However this has nothing to do with certificates. Indirect authentication can be done without certificates, like in Kerberos, or like in SSH if you have a management computer that you pair by copying the public_keys with every computer in the network. Later, whenever you want to enable some client to connect to a SSH server you use the management computer to copy securely the corresponding public_keys between the server and the client.
So no, there is no advantage of certificates related to reducing the number of transfers that must be done through secure side channels, like copying through a portable memory.
Certificates provide other features, like temporary validity and revocation, which can be useful in an enterprise context.