"Last Call Date" field - usage
I have checked the Online Help for the Last Call Date field and here is an interesting paragraph about it under section Calendar and Activities > Managing Calendars and Activities > Tracking Visits (Sales Calls) to Customers:
"If your company administrator included the Last Call Date field on your Account or Contact Edit page, that field is automatically updated on the linked account and all linked contacts. The update occurs when you change the call record’s status to Completed and save the record. The field reflects the start time and date of the call."
My understanding is that only for users having the field "Last Call Date" into the Account or Contact page layout , that field is automatically updated when you change the associated call record’s status to Completed.