Its a form of personal empowerment through delusional thinking secret knowledge.
Like their related ideological cousins, Tax Protestors (There is overlap between the two groups), Sovereign Citizens often base their ideology on intentional misunderstandings, wishful thinking, and open-ended conspiracy theories about the workings of government.
The principal virtue of this is a fundamental misunderstanding of political science, namely the belief that governments derive legitimacy through laws alone - that government is based upon what occurs on paper, or what they believe has occurred on paper, and this allows them to exert a form of control over the world if they can only “Beat” the system as defined in the paper world - that if one alters the documents, one becomes invisible to the hand of government. That if you don’t file a tax return or if do you do something like insert a colon in your name, this discombobulates the machinery of government so much that the “Bureaucrats” can’t come after you. This, over time, takes on a religious aspect for them - redemption - in which they are freed from the constraints of the corrupt and impure world.
One of the classic scenarios of this is the belief that if they have a drivers license that denies liability for accidents, then they do not have to pay for tickets (Which can lead to dangerous and potentially lethal encounters with law enforcement, but which are often very comical to watch, but taxing and stressful for the officers involved.) That they make these licenses themselves in a way that is templated off official state documents is one of many things that gets them in trouble.
And they generally believe these things work because someone they paid about $450-800 told them so in a “Seminar” in a manner that again, is not entirely dissimilar from how the heresy of Tax Protestors spreads.
That said, they are not inherently stupid, as they as a ideology are inventive and industrious in the arena of financial crimes - particularly because they rationalize the government - and by extension the financial system that it regulates and supports - is illegitimate, they express generally no ethical compunctions at all about stealing bank records, personal information (Again, a product of the government) and money.
But, they willfully attempt to exempt themselves from the jurisdiction of their government, a de facto renuniaciation of their citizenship, while often simultaneously demanding benefits from a government that they aren’t simply arguing is illegitimate (Rational people can do that, election fraud, etc.), but that can never be legitimate, and can never govern them even if it were, but whom they expect to provide them with human rights and extensive protections when they actually do get arrested. So they want to be Americans, mind you, they merely don’t want to be responsible for the nation.
Which is Heresy.
As an aside, the net effect of their activities isn’t invisibility or exemption. It doesn’t befuddle the bureaucrats or the authorities. It merely exasperates them and pisses them off. Its much akin to a mother having to chase her naked, heavily armed adult son around a carnival while he screams “YOU CANT SEE ME! I’M INVISIBLE!”
As a movement, I’ve never heard of its like anywhere else in the world.