The smtpd_client_restrictions is meant for all clients connecting to the server, not just clients that try to relay mail through the mail server, but also for local delivery. To have the mail server accept mail for all clients for local delivery, but require authentication for relaying you have to specify the smtpd_recipient_restrictions option. Here is an example:

smtpd_recipient_restrictions = permit_mynetworks,
check_relay_domains,
reject_unauth_pipelining,
reject_non_fqdn_recipient,
reject_unknown_recipient_domain,
permit_sasl_authenticated,
reject_unauth_destination,
reject_rbl_client sbl-xbl.spamhaus.org,
check_policy_service unix:private/spfcheck,
permit