Thank you, Jimmy, for the upvote.

I originally posted this in April 2020, it is now December 2020, 8 months later, so I've enough experience to provide an update.

Due to this issue combined with the confoundingly incredible failure to simply log someone in, we actually have little choice but to have our agents use email instead of Zendesk.

The scenario is like this:

We send screenshots as attachments in tickets with clear instructions how to access them
User can't log into our support portal (Zendesk Guide) because they use Safari
Images have no PHI so they wonder why we can't just send it to them directly
We can. Agents have to locate the email equivalent of the last message in the ticket, acquire access to the support channel, and send an email as that support channel...

I hope someone at Zendesk sees this and escalates the issue. We are literally having to resort to not use a Help Desk system for ourselves as agents as well as for our end users.

If that doesn't raise a red flag...

I can't imagine the level of effort being crazy either given that copy/paste is something already supported, it's just plain blocked, so it's not like they need to build a new feature.