When a user is provided with Support admin role, upon access to CH they are still able to see global org features for the purchased services.
Example: From services:
Upgrades & Migrations section
The panels are visible for the admin, even tough they do not have sufficient privileges to operate with them. Which accordingly results into >HTTP Status 403 - Forbidden pop up error - Correct behavior when the user is not full admin. (spark-admin)
The support admin idea is to provide access to reporting and analytics , and having additional features and services available may lead to unnecessary complications.