I don't think you can remove authentication part of SSH because you alway need a username to open a session but you can set a blank password and set
PermitEmptyPasswords to yes in your sshd configuration.
But this is not really safe, using keys authentication is better.
If you give your customers a public key it means that they can allow you to connect to their ssh server, not yours.
I think you want customers to connect to your ssh server. In this case customers need to give you their public key and you will allow them to connect. If all customers were using the same public key to connect to your ssh server it would mean that all customers use the same private key, and this is not an option (it's not your role to provide a private key and private key should not be shared)
Regarding encryption and snooping, encryption is done with session keys not public/private key, but to exchange session keys ssh use public/private key.
So if all your customers where using the same private keys, if they snoop a session from the begining they could decrypt the session, if they snoop the session after session keys exchange it would be very difficult to decrypt the session.
A good Article on how ssh works http://www.eng.cam.ac.uk/help/jpmg/ssh/ssh-detail.html