In the case of Bitcoin, the network can be the third party. That's what the 2-of-2 version is: both parties agree on the terms (that only further agreement from both parties will be accepted) and the network holds it until they're ready for disbursement. Of course, even with good intentions, the death of one party or HDD failure could lead to un-recoverable funds -- which is why I wouldn't recommend it for any substantial value. But if you're purchasing something for under $100, I think it's acceptable (and third-parties may not want to deal with small tx, anyway).
I don't see how that solves anything. If Alice wants to buy something from Bob for 10BTC, and Alice doesn't trust Bob to deliver and Bob doesn't trust Alice to pay, how does "the network" decide if Bob has delivered or not to know whether to sent the money to Alice or Bob? If Alice is "lazy", then Bob might have to wait until the contract n-locktime expires to get his money, which might be a long time. Worst case if the tx can't be finished without both parties signing it, then if Alice is lazy Bob might never get his money, and if Bob is crooked then Alice can't get her money back.
You're missing the point. People buy stuff all the time, from other people they don't trust over the internet. But for many transactions, they do it anyway, and just
hope they don't get screwed. This system makes it an order-of-magnitude safer to conduct these transactions. No one gets any money (or gets their risk deposits back) until both parties agree.
Both parties have an incentive to complete the transaction smoothly and without issue. It means that the seller can't send some super-shitty/incomplete product to the buyer knowing that he's already got the buyer's money. The buyer doesn't have to send money to some random person on the internet hoping that he's going to ship some potentially-imaginary product.
I highly recommend third-parties, but I think it should be possible not to use them. And people who use silk-road would probably agree with me (though I am making no formal endorsement of silk road or drugs in general: just an example of where executing transactions between untrusted parties may be desirable without a third party).
Plus, the benefit of using 2-of-3 is that there's a lower threshold of trust needed for the third-party -- there is no risk that they take the bitcoins and run. They'd have to collude with the one of the parties to do that. All that matters is that they are impartial to the two parties involved.
If you've figured out some magical way to do escrow without a trusted third party to settle disputes, I'd love to hear it, but it seems technically impossible to me. As I mentioned the best you're likely to do is to lock the money up on the blockchain so your third party doesn't need to be trusted to
hold it, just to release it to the deserving party. That's really not much better than what's possible now, although it might streamline things a bit.
You've missed a critical distinction here: there's a difference between "escrow" and "third-party arbitration." The escrow simply means that the money is held by a third-party that has no partiality towards either of the first two parties, and that there is an explicit agreement about the conditions under which the money will be released. "Arbitration" means that the third party gets involved to solve a dispute, which may involve contacting both parties, and sorting out semi-truths to find out who the money should go to. Typically, third-parties serve both roles.
In this case,
the bitcoin network can be that third party
escrow -- it is holding onto money for the two parties, and has instructions to release it only when there is a distribution agreement (spend tx) that is signed by both parties. You're right, the network can't arbitrate it: but it can be trusted to be impartial and not steal the escrow fund.
In many cases, especially early in the multi-sig world, there may not be good third-party services that both parties agree on. In that case, I'd prefer to use the network for escrow alone, than trust that some third-party the seller is recommending is truly impartial (
super-common escrow fraud).
As I said before:
(1) I only recommened this for
small transactions, in which case the third-party arbitration may be more expensive than the transaction itself. In lots of standard transactions, it doesn't even make sense to have a third-party, does that mean that we shouldn't bother at all?
(2) When neither party gets the money, they will (usually) find a way to agreeably resolve their own dispute so that the money does get unlocked.