alt Hacker NewsFor software development that's perfectly fine, and probably leads to less bloat etc., but in the example given it's an Emergency Room. "Make sure patent X gets operation Y" is a bit more important than "More rounded corners?". I know these are bad Kanban tasks but in some jobs you just aren't allowed to miss and just do the things "really care to keep track of". The other stuff is important too.
Your theory is that emergency room workers would think "make sure patient X gets operation Y" so unimportant that they'd just leave it off the board? I have more faith in them than that.
There is no job where all work is equally important, where all ideas are equally good. Even in emergency rooms, where triage is a vital concept. I think it's ok if finding a new poster for the break room gets dropped because there's too much work treating patients right now.