Power relations exist in practically ever instance of an interaction between two or more people, and politics concerns itself with the study and understanding of these relations. Understanding that power and politics exists outside of the boundaries of the state is important, because it sets the framework for an understanding that things such as who owns X or someone choosing to do Y can be deeply political. For instance, a patriarchal culture that gears women towards doing Z role in life could be considered to be a mere "choice" under your own framework, but understanding that it is a political action influenced by power relations blurs the lines between what can be considered a valid choice and what isn't, and it may for being rectified by an outside force such as the state. Now, of course, one might say that by de-limiting the state you open yourself up to political forces opposed to you that may try to impose their views upon you. But that's why, in such an instance, I'd side with whatever political group had the best chance of stopping the other group, be they minarchists, classical liberals, socialists, etc. But anyway, this is just an example, and you're free to edit the example to remove any priors that I've inserted that you disagree with. The overall point still remains though.
I also have little care for the arguments saying that I shouldn't force my views on others through the state, which is related to this but not exactly the same.