Imagine a bank on Ethereum that accepts deposits and allows withdrawals (first example here: https://learnxinyminutes.com/docs/solidity/ )
Anyone can deposit and withdraw, and no central party has the right to control the funds, if the contract is designed that way. As such, there is no custodial risk that the funds are stolen - and perhaps even no need to regulate the bank itself. (obviously, someone can steal if they get your private key, just not through the bank itself)
Lots of other examples. Bitcoin lets us set a credible limit of 21 MM, but in the real world you'd have to trust a central bank's word for the same.
Or the Lightning network allows peer to peer payments through counterparties. But none of these counterparties are able to steal the money midway through. This is akin to having 20 random people help you move a payment across the world, without any of them being able to steal the money.
Finance is full of these examples where we have to trust other parties, and crypto may have a huge impact there. Also, by reducing regulations and capital requirements, may make the space more ripe for startups to attack finance.
No crypto system can close trust beyond the network and it’s nodes. Some other dependency is required for that. Crypto might be shown to allow for some new kinds of dependency to step in at that point but I don’t know of anything like that myself.
They don't protect you from a third party not shipping your products that you bought on eBay.
If you have ever dealt with companies like PayPal as a merchant, you know why this is important.
With the distributed system, essentially we are trying to hardcode all of the rules, so there isn't any wiggle room for fraud, or a single person changing the rules on you, etc.
The downside to this, is that it means that it essentially becomes goverened by the software devs (or controlling body) of the altcoin. However, it sort of protects the consumer a little more by making it harder for a single governing body to make singular changes, because they'll want everyone who runs a type of exchange for the coin to participate as well so as not to alienate the coin and userbase...
I do think we're still a ways off before the blockchain actually gets mass adoption in terms of real world usage (instead of it being a speculative, get rich quick scheme that it is now to a lot of people)
Alice wants to buy something from Bob. But the only way to do so is through Eve. Then Alice and Bob both need to trust that Eve won't steal their credit card or money transfer in between.
Your question is regarding whether Alice can trust Bob (Not whether Alice and Bob can trust Eve the Middleman) There isn't currently a mainstream app that does this yet. One notable example is OpenBazaar, where they created a protocol to carry this out in a trustless manner, but they're just getting started.
 Under scam mitigation - https://www.openbazaar.org/blog/openbazaar-development-updat...
Trusted middlemen usually serve a useful function in the system but for some use cases (i.e. irreversible micro transactions), they’re too expensive.
The above distinction, I believe, is important - I’m not objectively better off using one or the other, it depends completely on which scenario I’m more worried about.