I think you are confusing object level satisfaction and meta level satisfaction. Despite many policy disagreements throughout the years, the American people have agreed for about 150 years that the current form of government is the one that should govern.
In other words, Americans want a participatory democracy/republic. Voting is an expression of support for that model - thus voting enhances the legitimacy of the current system.
P.S. For cynics and public-choice theorists, I'm not arguing that the United States is a participatory democracy - that's a discussion for another time. I'm only explaining why the act of voting adds legitimacy to the current setup.
Erm, I don't feel you've explained it though. All you've reiterated is that voting is an expression of support for the model, without explaining how that is.
Also consider that voter turnout can be highest when meta level satisfaction is lowest. Voter turnout spikes right before revolutions and civil wars; this is exactly people saying that they consider the system illegitimate and want it scrapped.
Related to: Voting is like donating thousands of dollars to charity, Does My Vote Matter?
And voting adds legitimacy to it.
Thank you.
#annoyedbymotivatedcognition