Is PoW and consensus unnecessary without double spending? Satoshi's whitepaper claims that the reason there must be a consensus on all transactions is to solve the problem of double spend. I'm curious then, how would a non-consensus based system work if double spend were not a problem?
If a coin is still represented as a series of transactions, each of which is verifiable, and these are submitted as proof of ownership during transactions, then how can one prove that the entire coin is valid? While no one can fake a spend from an unwilling party, it seems you could fake the entire coin altogether.
The only solution I see to above is that each coin is initially issued and signed by a trusted party. Once these coins are in existence the trusted party is removed.
The only solution I see to above is that each coin is initially issued and signed by a trusted party. Once these coins are in existence the trusted party is removed.

This is not correct. Why would that party need to be trusted?
Is the issue that they might sign more coins than they said they would sign? But that's a double spend problem. Right?
A double spend is when a party is only supposed to transfer X coins but they sign valid transactions to transfer Y coins where Y is more than X. The assumption we started with is that double spend isn't a problem. So there is no need to trust the &quot;trusted party&quot; since the only problem would be if they double spend and the starting assumption was that double spend wasn't a problem.
At every point in the system's existence, there has to be some set of future transactions that are valid and some set of future transactions that aren't and everyone has to agree on which transactions go in which set if they know the system's state. The system's initial state is also a system state, and so part of the system's rules have to be to see which transactions are valid from the initial state.
So simply a rule that there exists spendable tokens in the system's initial state is sufficient. The party that can spend those initial tokens doesn't need any special trust -- they are no different from any party that can spend any tokens in any other state.