You got it upside down. Exactly because too many people think like that, this whole corrupt system works. Imagine the whole country refusing to pay bribes. They would disappear tomorrow.
This whole "but this single action won't change anything " attitude may feel rational, and even be (selfishly) rational, but the effect comes through the aggregate. Lots of people in society behaving like that, and you get emergent properties caused by the aggregate of those individual choices. A dangerous (and pretty selfish) path to go in societies.
If everyone who has a problem with the corrupt system opts out, the system will chug along fine. Most people don't care, obviously. The people who make a moral stand will just be poorer and less able to thrive. You are basically suggesting something a lot like being Amish, they refuse to participate and as result they are a cute little subculture that is slowly disappearing.
So you're saying during Jim Crow people should have refused to build factories? I don't follow your point, laws which attack black people are very different from bureaucracies that require bribery to give you permits for your business. I mean both are bad, but they are very different, and Jim Crow is a thousand times worse, both because of it's basic nature and because it was the law of the land and enforced with the full power of the government (vs corruption, which is people sneaking around in violation of the law).
This is what you are doing: "So you think it's ok to just pay it when the police to give you a speeding ticket when you weren't speeding!? That means you are fine with the holocaust!"
At the end of the day you are only playing a game that someone else has made. It can be corrupt, terrible, whatever, but the fact is you can do nothing to stop it, so if you want to get anything done you need to play the game. Your little petty protest does not stop the game from being played, the people who made the game as it is just don't care about your opinions at all.
This whole "but this single action won't change anything " attitude may feel rational, and even be (selfishly) rational, but the effect comes through the aggregate. Lots of people in society behaving like that, and you get emergent properties caused by the aggregate of those individual choices. A dangerous (and pretty selfish) path to go in societies.