Considering viruses, and more security/clipboard trackers are coming into being we should have a on/off switch constantly visible (and toggle-able) that explicitly turn the clipboard sync on/off independent of the "Suspend my Input" function.
It's only a matter of time before clipboard monitoring for passwords because a standard feature of the malware suites.
Something like:
We have seen security issues related to this. Multiple techs connected to one target machine, and the clipboard becomes shared even if SC does not have focus. This means SC will insert tech1's clipboard content into tech2's clipboard. Well intentioned, but not good.
The ability to toggle clipboard sync on and off from the host client has been registered as a feature request. Just want to add, though, that globally disabling clipboard capture is an app.config setting. On a cloud instance, you can download the Advanced Configuration Editor to access this setting.
Hope this helps!
As of 19.4, the host client now includes a toggle to control clipboard sync!