Fascinating post.
Why do such companies not already exist? Because the State would use its superior power to put it down. Such a company would face the same problems as a secessionist community defense agency. Essentially you are saying a non-territorial secessionist community is more likely to be created and sustained than a territorial one.
How could such a company succeed? Either 1) the defense-against-the-state (DAS) company has superior firepower (unlikely) or 2) the State does not engage with the company. For the latter to happen, there would need to be widespread support among the dullards for the secessionists and the DAS company. Right now, the dullards would be on the side of the State; the secessionists would be denounced as unpatriotic tax evaders, and the DAS company would be called terrorist.
The likelihood of a DAS company being created depends on the profit margins involved and the risk of State aggression. So as taxes are increased, the likelihood increases, because the company will have bigger potential profits. It could promise to only ‘tax’ 70% of income, for example, rather than the State’s 80%.
There already exist some individuals who refuse to pay taxes. These people presumably have some sort of mutual support network for ‘how to get away with it’ and ‘what to do if the State goes after you’. The development you are describing would be an evolution of this network to the point where it is done openly and where dullards join without fear that they will be punished by the State.