As someone who has been reading the Cap comics since Gruenwald was writing him (1985-1996) I'm WELL aware of the differences between the MCU portrayal and the comics. But it is clear to me, with that last statement you made, that YOU aren't.
Here's a refresher of how well Steve works with the government (otherwise known as Steve Rogers' greatest hits in telling the government to @#$% off):
Englehart (Nomad: Man Without a Country story arc):
Gruenwald (Captain America No More story arc):
Millar (Civil War story arc):
And, if not for the three image limit I could post panels far more recent than the above. He basically told the American government, through Ross, in the current Avengers run under Jason Aaron that he doesn't work for them and that the Avengers do not belong to any one country and refuse to be the US government's lapdogs.
So, CAN Steve work with the government? Yes. Does he like to? No. Does he do well in that role? Also no. You're confusing Steve with John Walker. Moreover, readers like it better when Steve beats to his own drum, thus the reason no one liked the 1950's portrayal. The above stories (Englehart, Gruenwald, etc.) are considered some of Cap's greatest hits. There is a reason for that.