Has anyone had to do this? How did you go about it? The nut to crack being that only the agent itself or a supervisor is actually allowed to change agent states, not an admin. Consequently, the only way I see to do this would be to create one big team just for this purpose.. every agent gets added to it, and your "admin" user would be made a supervisor. But I guess in large systems you could run into scaling issues with that approach.
So, how do you handle that if you cannot go and gather user passwords?
I don't think this is possible. You touched upon and are correct about all of the roadblocks to get this solved. I wouldn't recommend having one big team if it is a large system for the scaling issues you already stated.
Alright then.. so here's my feature request: create an admin role that is permitted to do such things. Should be easy enough.. simply remove the "is agent itself or supervisor of" and replace with "what I said before or is an admin".
Like I mentioned before, Finesse isn't meant to be a monitoring/admin tool. Its purpose is to be an agent/supervisor desktop, which is why it doesn't have the feature for an admin to be able to change the agent's state.
That being said, you are free to open a feature request, but this forum is not the right place to do it. I will reply to your ticket with the information.