Our armed forces were not immigrants obviously, so the analogy is flawed. My Dad spent a bit of time in NZ.
There is a key difference between a visitor and a person who aims to stay for a longer period of time. In the Schengen Zone, you can stay legally for 180 days (I think) and then you need to leave, and only for visitation, and some minor business stuff.
This is why they check you when you depart, you go through (e)immigration once again.