Don't set PasswordAuthentication=no here because the connection plugin will do that unless a password is actually specified with -k/--ask-pass.

examples/ansible.cfg

@@ -145,7 +145,7 @@ filter_plugins     = /usr/share/ansible_plugins/filter_plugins
 # will result in poor performance, so use transport=paramiko on older platforms rather than
 # removing it
 
-ssh_args=-o PasswordAuthentication=no -o ControlMaster=auto -o ControlPersist=60s -o ControlPath=/tmp/ansible-ssh-%h-%p-%r
+ssh_args=-o ControlMaster=auto -o ControlPersist=60s -o ControlPath=/tmp/ansible-ssh-%h-%p-%r
 
 # the following makes ansible use scp if the connection type is ssh (default is sftp)