the database system to store any value associated with such external writes temporarily in a special relation in the database
Can't we behave with these values like other values?

That's exactly what is suggested in your quote: you store data to be written externally in a (special) relation, because they are special, transient entities.
Suppose you have a workflow system in which a task is assigned to a user by updating its user_id attribute (&quot;internal write&quot;). It also needs to send an email notification (an external write) to that user. These two happen asynchronously, but the external one must always happen after the internal one is persisted. You update the task record as usual (nothing &quot;fake&quot; about it) and create a new outbound_email entity with whatever information is relevant. When the task update is committed, you process outbound_email and delete the transient record.
This works pretty much like a write-ahead log for external actions: you first create a record for the action, then perform that action at an appropriate moment, then discard the log record as it is no longer needed. If the flow is interrupted, you replay the &quot;log&quot; to recover.