There is no such setting, or permission set to be applied. The administrator role is the only one that can set a default template for other users to use. What you can do as a workaround is to create a few administrator users and restrict them by user( not by role) to some permission set you want them to have. This will enable the users to set a default template and still restrict them to some other functionality you do not want them to have access to.
Ivan D. Dimitrov
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