Where this becomes interesting is that someone can just change the past data, then go through and update all the subsequent additions to come up with a the new final value. CT handles this by having multiple other entities check that the CT root values are not changing over time. Git handles this by allowing for similar mechanisms - if you believe Linus he memorizes the root hash of his local repo before bed each night. A post-it note would work just about as well for the Linus/Git case, but I am getting off topic.
I don't see value in proof of work because it assumes that any system would have more entities (where each entity has some amount of computing power..) watching than there is computing power attempting to rewrite it. That doesn't really scale up across most industries use cases. A set of say, mortgage companies, could just exchange data in a merkle tree format and raise an alarm if it looks like the values changed from the prior root. This is very fast and cheap to compute and doesn't require proof of work calculations.
I'd agree the Merkle tree is good as the ledger. AFAIK it is also used in certificate transparancy logs: Every block of log entries contains a cryptographic hash to a previous block, so you can't rewrite log entries, only append them. This is what guarantees honesty in the certificate world, and is I assume the only aspect you need for your proposal.
But the Proof of work is basically a race to do as much computation as possible. This is the part that wastes so much energy and resources, the part that slows things down, but also the part that provides value to cryptocoins by proving that someone wanted to waste/spend the resources.
Do you see value in a system that has both aspects?