> That's entirely insufficient, as it doesn't prove that the chain you have been given is genuine. It just proves that each transaction is signed by someone holding the right signature. Nothing in your scheme prevents multiple diverging chains. The entire point of the confirmations etc. used by blockchains is that not only each individual transaction can be verified as coming from a specific source, but that the chain as a whole can be verified to meet certain criteria - specifically in the case of e.g. Bitcoin, the criteria that it represents the view of the majority of the mining power of the network.

No, this is wrong. I can sign a chain of transactions (Merkle tree is used in BTC as well), and you will know it came from me. If I'm a central authority, I can keep signing it in all of perpetuity, and it will be verifiably from me. As long as you trust the signer, it's very simple.

The reason Bitcoin is different is because you want to be able to have different signers doing each block. The way bitcoin does it is through clever incentives: miners only believe that other miners care about the longest chain, and they want to sign that last block because then the other miners will recognise their mined coins.