May I request that if you want to have a discussion about theory behind graph models for transaction state, that you create a new thread and we will discuss it there. Then after we reach mutual understanding, we will post the summary back in this thread. I don't want to make this thread unnecessarily noisy.
I don't think trees will work and that is why I think we will end up writing a long discussion. And this thread is already getting difficult to follow, being too long to digest holistically in a reader's mind.
This is not specifically about trees; it could be any single, completely linear sequence of chained transactions. In fact, I think the reader would be enlightened by the answer to this simple, direction question about trustless consensus:
Why is it not enough to find one global sequence for all transactions ever made?As I see it, sequencing is all you need, even in the face of double spends because the first time an output is spent in this linear sequence, subsequent spends of the same output will simply be invalid.