I haven't read this entire thread yet - it looks pretty long. So I might be saying things that other people have already said before.
Anarchism could matter more to this theoretical person in the future. Life is everchanging. Something could happen, some kind of crisis, that would erode this person's quality of life.
For instance, a family member could get a disease, one of the preventable diseases which is directly caused by the modern lifestyle. As they research the disease and find out that it was caused by something in the modern lifestyle, they might become aware that this should never have happened, and they might care more about fixing the world to make sure that it doesn't happen again. There are many health problems that are directly the result of the drug industry and the government-controlled healthcare industry. This person might become aware that their life would have been better if they had not been forced, or deceived, into using government-controlled healthcare. (I won't be specific about which health problems are directly caused by the government's healthcare system, because that would sort of derail the thread, but if anyone wants to know what I'm talking about I can explain.)
Or, an economic collapse could happen. The collapsing of the economic system is an inevitable, recurring event. It will happen again and again and again, every few years, because of the corruption of the government-controlled economic system. This person might lose his entire life savings when his retirement fund gets destroyed. Decades of work can vanish in an instant if something happens to the economy. This could lead the person to think more deeply about how the economic system works, which could lead him to question the government's control of the economy.
This person might lose a loved one in a war. One of their children might go off to war and get killed, and it might cause the parents to think more deeply about whether or not the government's wars are a good and necessary thing.
So, anarchism might not matter to this hypothetical person at all right now, but life is unstable, and everyone is vulnerable to being harmed by the government. Government is actively harming people in many ways, in many places, constantly, every day, in ways that are sometimes insidious and hard to see, or big and obvious ways that are easy to see. The harm done by government is like a time bomb waiting to go off, maybe, or like mold rotting away the foundations of a house - it's there, slowly growing, and someday it will cause the rafters to break and cave in. The need to protect yourself against the government is a very real, physical thing, but people aren't aware of it until they experience it. There is always the potential that something will happen in the future, even if they are contented and safe right now. And when something goes wrong and they try to trace the causes, they might learn about some of the problems that can be traced directly back to the government.
I just thought of something else. They could meet someone and fall in love with that person, and their opinions could change because of this love. Sometimes falling in love can show people a different way of seeing things.