When you go shopping and choose from thousands of products, just like that, do you wait for anyone to force you into buying anything? There are some manipulative marketing attempts, but in the end you are the one who makes a decision.

I'd argue that this is not the case for most people.
Yes, if you are mindful about the systems trying to manipulate you, and consider it important to look out for your interests, then you will make the optimal decision. But most people I know will just choose the product that is marketed the right way for them, even if it's rationally a suboptimal decision.
And the world is full of such systems manipulating you, some of them so deeply entrenched in our culture/society/conventions that it's really hard even to become aware of them.
Anarchy is not a political system that will suddenly be enacted one day in place of whatever was there before, it's just the eventual outcome of people becoming conscious of themselves and their surroundings and making rational choices.