Currently only Accounts, Contacts, Leads and Users are eligible to be Activity Parties in the Required Attendee, Optional Attendee fields on the Appointments and Custom Activities.

It would be great if there were a flag in the Entity properties that would contol if the entity (either standard or custom entity) can play a role of the Attendee on Activities.

The Attendee field does not necessarily have to be taken literally here.
The Attendee fields allow multiple values (something the Regarding field does not do) and as such can play an important role in linking records in much broader range of scenarios.

Using Connections as a workaround would not be a good fit here as the overall goal is to display the Activity where it belongs, in the Activity folder, not in the Connections folder.