Security concerns on SMTP in SQL Server
The security concern with SMTP from a database server is the potential for disclosure of sensitive information.  For example, a user that has (or gains) permissions to execute sp_send_dbmail could send an email with sensitive information.  Disallowing outbound access to the default SMTP port is a security measure security folks sometimes insist upon to limit such exposure.  It is common to lock down overall database server network traffic in an environment with particularly sensitive information such that network connectivity is allowed only to ports/hosts specifically needed, and permitted only after approval by the security department.

You need to work with your security team if your organization does not yet have an infrastructure for database administrative alerts.  They may allow a security exception for SMTP if there are additional measures in place to prevent ad-hoc email access on both the database and SMTP server.