We are needing this functionality as well, for a good reason too, to protect the users of the service. There are some legitimate use cases for this across the health industry, emergency services, debt collection agencies etc.
One suggestion that was provided, which may be ok for some, is grabbing a pool of DDIs, and randomising which one is used as the outbound CLID, then change them out every few months. Unfortunately, in our case, this is not going to work, so we are a bit stuck for now.
This isn't possible and from what I have seen AWS are unlikely to change this, as they seem to be big on avoiding spam, either emails, sms or calls, coming from within AWS.
Is there a good reason to have the number set to private? Can you not just claim an additional number and then set a contact flow that says that the number is not active, or some other message?
I would reach out to support for this request as that seems like a perfectly reasonable request.
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