TL;DR:
* <PERSON> only ever does what he believes to be right, and many times, this does go against orders and the rules of the system, as evidenced by previous movies even before Civil War. He will break the rules if he feels it is the right thing to do, and he has faith in his own judgement and reasoning.
* <PERSON> initially remains completely independent, but after repeated attempts at doing the right thing which ended up causing more harm than good, he is desperate for some form of control, for someone better at this to tell him the right thing to do. In this case, that someone is a UN council.
Full Answer:
Prior to Civil War, it is true <PERSON> seemed to cooperate better with the system. He was very keen on enlisting in the army during World War 2, he was selected to join the Avengers and agreed with it, and later he got on <PERSON>'s case about keeping <PERSON> secret from the rest of the Avengers. However, there are a few points you missed out, especially referencing Captain America: Winter Soldier.
1. Although he enlisted in World War 2, it was not entirely out of patriotic fervor. As he said to Dr <PERSON> before he was accepted, he "did not like bullies" and didn't care where they were from. This lead him to attempt to enlist 5 separate times under false names, basically lying on his enlistment forms. He knew what he wanted to do was morally right, and didn't mind breaking rules to do it.
2. Later, on his tour as <PERSON>, this quality of his was further shown by his rescue of <PERSON>. He was ordered to remain at the camp. But he knew there was a chance of saving his friend, and so went against his orders. Enlisting the help of <PERSON> and <PERSON>, he went behind enemy lines and saved <PERSON> and his men. Again, he knew what he wanted to do was morally right, and didn't mind breaking rules to do it. Then when he returned to the camp with the men he saved, he knew the morally right thing to do was turn himself in for disciplinary action for breaking said rules, and that's what he attempted to do.
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In Avengers 1, <PERSON> was selected to be a member of the Avengers, as you mentioned. However, it may be noted here that again, it might not have been out of a desire to cooperate with the system. He had just woken up from a 70-year nap, all his friends were gone (he didn't dare call <PERSON>, afraid of her seeing him still young), and <PERSON> was telling him that the very same cube he had given up his life to deal with was back and causing trouble again. It is highly likely that, given a chance, he would have gone after the damn thing anyway, with or without the Avengers.
4. Also in Avengers 1, there was the scene where the Avengers realise how much <PERSON> had been keeping from them. Even lying to them. In the lab with <PERSON>, <PERSON> plants the idea in <PERSON>' head that something was off about <PERSON> and SHIELD. Later, <PERSON> hacks in to the system, and <PERSON> finds weapons that SHIELD had been developing, using the Tesseract as the power source. He realises that <PERSON> and SHIELD had been lying to them from the beginning and, though in the end they are all distracted by the threat of <PERSON>, <PERSON>' faith is still shaken by the lies.
5. In CA:WS, this is where his faith in the system was completely destroyed. After <PERSON> had been dealt with, and the Avengers temporarily disbanded, <PERSON> signed up with SHIELD and participated in many covert operations, alongside <PERSON> aka <PERSON>. We see the very first operation in the movie, where <PERSON> thinks the mission is to save hostages, but he learns that <PERSON> had been entrusted with a separate secret mission of her own, which was to copy data from the computers onto a memory stick. Later, he tells <PERSON> that he "can't run a mission when his men have missions of their own" and "soldiers trust each other, that's what makes it an army, not a bunch of guys running around shooting guns". <PERSON> attempts to placate him by showing his the Helicarriers meant for Operation Insight. <PERSON> is unconvinced, and later talks to <PERSON> about how complicated the politics of the current 'war' are.
6. Of course, as the movie progresses, we see the emergence of Hydra as a parasite lurking in SHIELD from the beginning. 569