You have the option to provide support to your customers exclusively via emails. Please follow the steps described below to provide email only support.
The following steps will give you the option to provide support to your customers only by sending emails to the configured mailbox:
Helpdesk Settings -> Mail Setup -> Email Support and select Enable button if it is not selected already.
Make sure Mailbox Reading and Reply via Email options are enabled.
Select Disable and save the changes. Disabling Web Support and keeping Email Support enabled will hide the ticket's web user interface from your customer and they'll not receive the ticket's link in any email communication with the staff members in Helpdesk.
With the above Settings, WordPress users will not be created for the customers. Only their Helpdesk contacts will be created.
With the above Settings, customers will not be able to access the tickets even if they are registered on your website. They will not able to access support form and will not be able to view the ticket's web user interface even if they stumble upon the ticket's link.