In the current form for banning these are the options:

During the chat

From the chat window, select Ban Visitor from the Actions drop-down menu.
Optional: Enter a reason in the Reason field.
Optional: If you want to also ban the visitor's IP address, select the Also ban visitor's IP address check box.
Click Ban User.

OR

To ban a visitor by IP address

From the dashboard, select Settings > Banned.
To add a visitor's IP to the list, click Add Visitor.
Enter an IP address and a reason.
Click Create Ban.

If a Supervisor or Manager is reviewing chat history and see there is a visitor that should be banned from chat they cannot ban unless banning the IP.
IP banning is not the best solution as this will ban ALL end-uses in the IP.

Most Users do not have access to ban via API

I would be very helpful if agents and other roles could ban post chat by means other than IP.

In Zendesk Support it is possible to Suspend access for a visitor, what can this not be extended to Chat?
All the visitor's information is stored in ZenDesk

Option # 1

If I am on the ZenDesk Support page and from the drop-list, I select suspend access. I should have the option to suspend access on all platforms I am using to communicate. IE Chat, Support, Talk, Guide....ect

Option # 2

From the chat window settings > Banning

Instead of having 'Add Banned IP Address'

have the option to ban via IP, Email, or Visitor ID
Enter a reason in the Reason field. should be a required field

Assignee should be profiled from the current user's account and the field is disabled.

Thanks for your time.

If you need any additional information to my rough notes, please feel free to contact me
Lance