Regarding third parties, on a blockchain you don't have to trust them to hold your money. You can set up a 2-of-3 scheme where if the two primaries agree then the third party never gets involved, and if they disagree then the third party decides where the money goes, and only then gets a cut. Advantage: in the absence of a dispute, this system is free.
Since when is the blockchain free? You still have to pay a transaction fee.
And with your scheme there's still the problem of how do you scale it? Even if you hope that you'll be able to settle the transaction without disagreement you still have to select a third party "just in case". I can't see working at scale unless you have "professional" third parties with good reputation who will be able to oversee a big number of transactions without being tempted to cheat the system. Why would these third party accept to work for free?
Maybe those parties would accept to be paid only in case of dispute but in this case (if the number of disputes is a very small proportion of all transactions) they'll probably ask for a significant amount of money to break even. You want this third party to be very reputable and hard to corrupt after all, that means that they must have a significant amount of money at stake. You don't want some dude doing it as his weekend project in his basement.
Furthermore the one contesting the transaction will have to be the one who pays the company because how could they force the other one to give money? In turns that means that this neutral third-party becomes biased, it has an incentive to side with whoever paid them to weigh in on the transaction since they've effectively become their customer.
That's kind of my problem with this entire blockchain thing, people are reinventing the wheel, telling everybody they're going to "kill the banks!" but they never stop to wonder why our current system works the way it does. I'm not saying that things are perfect as they are but if you don't learn from past mistakes you're doomed to reproduce them.
Yes, there's the standard transaction fee, but on Ethereum that would be about a penny. My point is there'd be no fee to the third party, in the absence of a dispute. In that case the third party would do no work. They don't even have to know about the transactions where they're designated "just in case."
The fee when there is a dispute would have to be higher; I'd argue that this isn't terrible, since it gives the primaries a stronger incentive to work things out on their own.
Obviously it would help to have some kind of reputation system for arbitrators. That doesn't necessarily have to be on chain; anything that lets both primaries agree on an arbitrator is fine.
The contract is what forces the payment; the money in question is held by the contract, and if the arbitrator makes the decision, the contract automatically deducts the fee from the held funds and pays it.
You're right that sometimes people ignore why the current system works, but the flip side is dismissing blockchain solutions without first understanding how they work.
Free? Who pays for the blockchain? Last I looked into it, each transaction requires about enough electricity to power a house for an entire day. That isn't very free.
That's an average including all the mining rewards, it's not actually paid by people issuing transactions. A simple transaction on Ethereum costs about a penny.
I agree the energy consumption of present-day blockchains is a problem; hopefully proof of stake will fix it.
