Why does WITH SECURITY_ENFORCED throw "Insufficient permissions" when querying EmailTemplate in Salesforce?

I’m trying to query the EmailTemplate object in Salesforce with WITH SECURITY_ENFORCED to respect CRUD/FLS, but I get an error even though the user has access to Email Templates.

List<EmailTemplate> templates = [
    SELECT Id, Name, Subject, Body
    FROM EmailTemplate
    WHERE DeveloperName = 'Offer_Letter_Template'
    WITH SECURITY_ENFORCED
];

{
    "error": "Insufficient permissions: secure query included inaccessible field",
    "success": false
}

Why does this error occur even when access is granted?

I wrote a SOQL query on EmailTemplate with WITH SECURITY_ENFORCED because I wanted Salesforce to automatically enforce CRUD/FLS.

I verified that the user profile has access to the Email Template object and the queried fields (Id, Name, Subject, Body).