you don't eliminate #1, it just has less consequences for the hosting provider.
Bitcoins can still be stolen (albeit perhaps not as easily as credit cards). But since there's no chargeback system, the victims don't have much recourse.
The expectations that we'll eliminate 100% of fraud are fundamentally flawed. Fraud will always exist. The Bitcoin blockchain provides a good amount of fraud resistant technologies that can be used by external systems to help lower the incidences of fraud in their own systems. Unfortunately, some systems that have connected to the blockchain have been vulnerable to being broken into, which is where the coins usually get stolen. It's companies like Coinbase and Blockchain that carry that responsibility for the rest of us, and for that, I'm grateful.
I would hazard the amount of fraud will go down considerably (compared to credit card fraud) once we've sorted around the best practices for securing your coin.
Isn't the problem of someone breaking in and stealing coins avoidable in the 'selling sth. for coins' scenario by just looking for incoming payments to a particular address, but without ever keeping any secret keys on a live system?
Bitcoins can still be stolen (albeit perhaps not as easily as credit cards). But since there's no chargeback system, the victims don't have much recourse.