Q: This explains how to block calls from numbers that are displayed. But how do you block calls from unknown and private calls

You can't. Contact your carrier to see if they offer that service.

Carrier AT&T is unwilling to assist in blocking calls with no name or number.

I believe there is a solution wherein only calls from your known contacts will ring on your phone and all other calls, including unknown callers, will be redirected to your voicemail.

Use your Do Not Disturb feature to only allow calls from known contacts.  Other calls will be immediately directed to your voicemail.

• Settings
• Do Not Disturb
• Select Manual
• Select "Allow Calls From All Contacts"

Remeber to check your voicemail and add new contacts as appropriate.

Is there a way to do it without blocking all text messages.

That is not completely correct. However, the use of Do Not Disturb will block more than just phone calls. It will block all notifications. See this support document with information about Do Not Disturb. https://support.apple.com/en-us/HT204321

Using Do Not Disturb is not the way to block unknown or private callers. At this time there is no way to do that on the iPhone. Call blocking is based on the phone number, and without that information coming in the Caller ID, there is no way to block it.