I'm sold on most of the Bitcoin aspects. I believe that the blockchain has incredible potential value and how the fact that it's decentralized removes a lot of the corruption and cronyism that are rampant in today's centralized institutions. However one thing I don't get is how does the contract, or property or other value that you have stored in the blockchain is enforced? Surely some people won't care that the proof of property of your land is in the blockchain and just claim it with guns. What do you do then? How is this sorted? States have judicial and military power. What does the blockchain have?
The blockchain itself does not have any power. It is just public set of records, like a phonebook.
Depending on the contract between trading parties, you arbitrage the contract disputes within the legal means you have available.
However, blockchain can act as a proof of agreement and everything signed there is very hard to forge: the other party cannot claim they did not sign the agreement if the private key used in signing can be proven to belong to the party.
The blockchain survives by having nodes which continue to keep it up to date which implies having a network which allows those to communicate.
As far as the question of someone ignoring the blockchain, since all transactions take place in the blockchain there is no such thing as a bitcoin transaction apart from the blockchain.
To put it in other words proof of ownwership of bitcoins requires two things.
1) Here, look, I have a private key. 2) Here, look, the blockchain says that this private key has some quantity of bitcoins associated with it.
In this context since the bitcoin nodes keep the blockchain correct, the only other way of obtaining bitcoins is via the obtaining of a private key by force, theft, whatever.