Just to sum it up then. You have already tried this:
1) run # plesk bin subscription -u example.com -mail_service true
2) Enabled the mail service in the service plan associated with the subscription
3) Verified that in the service plan of the subscription the number of mailboxes is set to a number greater zero or to unlimited
4) Synced the subscription with the service plan
Let us try this please:
- Go to "Tools & Settings" and verify that you have a "Mail" and a "Mail Server Settings" menu
- In the "Mail Server Settings" item, please make sure that the checkbox "Enable mail management functions in Plesk" is checked
- Go to "Tools & Settings" > "Server Components" and click "Refresh"
Does it work after that?