They have so much different missions that I would not be able to put any overlap between the 2 functions beside who eventually pays for them… What kind of shitty experience has led to such a take? Care to share some?

I grew up with my father being an officer in firefighting in Europe (not France though) and my perception is way different. Among other things he escaped death quite a couple of times just to extract some poor souls from certain death situations, helped the community avoid disasters and generally be super kind about risk prevention visits…

He was a totally absent father though but I chalk that to his commitment to the local community.