I still don't see much logic behind what you say. Ultimately it doesn't change anything from where you start and instead of one "law provider" you get by choice of majority another with brand new laws and some part of the population disagreeing with them...
No, it means I look out into the marketplace and I see law and security provider 1, law and security provider 2, etc. Just like I see ISP 1, ISP 2, etc. I then look at the deals that they offer and then how much it costs and make my choice based on that.
The difference, of course, between free market providers of law would be that they would not be my rulers, just as ISP companies don't rule me. They are trying to get my custom with the best possible deal they can offer me. I get to choose.
Can you imagine what it would be like if there was only one ISP in the entire country? Do you think they would offer a good deal?
What does this all have to do with anarchy?
Are you sure that you know what anarchy is? It doesn't mean chaos.