I do not want to disable the Employee Request Letter feature by selecting each letter template individually. Is there any other quick option available?

Yes. You can disable the Employee Request Letter feature in one go by performing the following actions:

1. Navigate to Settings > USER ADMINISTRATION > User > User Roles. 
2. From Category drop-down list, select Letter. 
3. Go to Employee Request Letter and clear the check boxes under Read Acess and Write Access.
4. Click Save. After you click Save, the request letter feature will be disabled for all the employees.