Government is just people trying to do triage, discern signal from noise, coordination, move the ball forward... with a bunch of other people.
People expect too much. It's amazing anything works at all. We should all marvel at the progress we've somehow achieved thus far.
While striving too do better, of course.
The motivation you suggest may apply to some people, sometimes, in some places but certainly not all people in all governments much and perhaps even most of the time.
Self interest, corruption, the desire for power, the desire for conquest and theft and a complete disregard for their citizenry and indeed humanity in general are unfortunately all too common with those who get into the governance business.