You would check a new address really had funds by asking the network for the branches concerning just that address.
Even if the majority of nodes withheld information you would only need one honest node to get the complete picture in a short download.
How would that compare to maintaining a merkle tree with an enforced sort order: sorted by address? Then the odds of accepting an answer from a lying node would be zero. No need to seek a consensus.
My solution did not seek consensus, as I said once you have the branches with transactions linked to the main hash you KNOW they are true.
Even if 90% of the network is withholding the "spent it all" transaction you would easily be able to get it from just ONE honest node.
How is the alternate merkle tree even safe with no/little mining? I could make a false log, sign it with minimal mining or put it in the blockchain (both easy) and fool you all right?
My solution had further advantages as NO ONE would need the full block - a big advantage as miners can't run lite nodes as it is.
My solution also solved propagation time problems blocks have today - this solution would not as it relies on the normal blockchain.
All of this without forking or merged mining.