I am not an engineer, but have a good friend who is an engineer doing nuclear reaction cooling systems. He worked in the industry for close to ten years before getting his PE, and only did it because his employer asked him to (I believe it helped them get a contract). Based on my conversations with other engineers, other industries (ME, EE, CE) seem to operate in the same way--some employers don't require the exam at all, others may push to have employees take it within some period of time after hire.
Right, because PEs usually play out in higher-level industrial "type" projects. Government, I think requires PE/FE in a lot of situations. The other part of this, is that you take the PE/FE exam TWICE when you leave college. One is right after college, and then you work under a PE for 5 years (if I'm not correct) as a "mentor" then take it again after 5 years. You have to be registered under this PE, as well. The certification is like the other applied engineering disciplines - where it says you are accountable for what you make. But you already seem to know this from side conversations.