Anarchy means: without rulers, not without rules. People can agree each others without rules, based on direct agreements and common basic rules. Bitcoin have very direct rules, without any ruler, so by itself is an anarchist protocol.

So yes, Bitcoin in the end will lead to an anarchy. As I explained in one of my guides: https://darthcoin.substack.com/p/natural-law-and-bitcoin

Anarchy is derived from a Greek word and really means "having no ruler," but rather "a community consensus".

To apply the term "anarchy" in relation to Bitcoin, I think decentralization by Bitcoin, promotes economic freedom, as it enables people to organise their own economic affairs autonomously.

Bitcoin's decentralization, will somehow lead to anarchy, but in a positive way.

anarchy does not form from a system that has evolved beyond anarchy. Small experiments like the Seattle Chaz/Chop situation demonstrate how broken anarchy gets as the population gains enough mass to have differing opinions—it broke down because the group couldn’t even agree on how to define itself after it had quickly mutated to the point of having a committee run marketing for it. Anarchic social systems evolve into having some members lead others. It’s hard to imagine a society where everyone is so equal that nobody would govern anyone else—even in a bitcoin powered economy, there will be leaders and sheep.

I hope so

It likely will. But in a sense, we already live in an anarchist society. For example if police come to arrest you for growing cannabis, you can always get your bazooka out and defend yourself against the aggressors. And you'll realize no one rules over you. Then you'll probably need missiles to fend off the helicopters and fighters that will undoubtedly follow. Most people, out of convenience or a lack of resources, choose not to.

Bitcoin will likely change the balance of power and weaken the state, and make our right to defend ourselves from NAP-breaching aggressors more enforceable.

Trade leads to the absence of violence

Bitcoin leads to great global liquidity and the possibility of commerce

Therefore, peace will reach every corner of the Earth automatically

Hopefully just limited government that actually follows classical liberal constraints. I'd rather not do total anarchy

I hope so.

I don't need any big brother rule over me; and anarchy is not that bad, a recent example is Kowloon Walled City in Hong Kong.

If we're clear about our definition of anarchy, and haven't been tricked into thinking it's something to be feared.

Anarchy from people disagreeing? Or nation states fighting for control over their citizens?