I pretty strongly believe that "blockchain" is a misnomer given how much the structure relies on Merkle Trees. Forks aren't some aberration in the data structure, but a direct exploration of branches in the Merkle Tree. Most blockchain algorithms, Proof of Work especially, are just very rigorous "rebase operations" in git terms.
Blocks are not organized into merkle trees in Bitcoin. Full nodes pick the longest (PoW wise) valid chain and discards any other competing chains and their blocks.
There are some alternative cryptosystem designs that do take blocks in "losing chains" into consideration using a DAG structure, like GHOST and its successor SPECTRE (by Aviv Zohar et. al). Ethereum also has a concept of "uncle blocks", which are rewarded and contribute to chain selection.
> Blocks are not organized into merkle trees in Bitcoin. Full nodes pick the longest (PoW wise) valid chain and discards any other competing chains and their blocks.
That's pretty much the definition of "rebase" and again, that's a functionality of the algorithm on top of the data structure (Proof of Work) not the data structure. The raw data structure is still a merkle tree even if in practice the algorithm suggests to people there is only one rebased trunk. But even that isn't entirely true in practice because there are still multiple rebased "branches" among the Bitcoin forks such as Bitcoin Classic, Bitcoin Gold, etc. All of those are branches that share the same conceptual merkle tree. Even if they aren't "Bitcoin" that's more of an algorithmic and political distinction at that point, not a technical one by means of data structure. It's not the data structure that makes it a chain, it's the algorithm and the politics, hence why I think blockchain is a misnomer for the data structure itself.
Are you sure you mean merkle trees specifically and not just a tree structure in general?
A merkle tree is a very specific type of hash tree, which Bitcoin only uses for transactions and not for blocks. Merkle proofs are used to prove that a txid exists within the root hash committed in the header block. What would be the reason to organize blocks into a merkle tree? What would that let you prove?
> here are still multiple rebased "branches" among the Bitcoin forks such as Bitcoin Classic, Bitcoin Gold, etc. All of those are branches that share...
Bitcoin, BCash and BGold each have incompatible rule sets; A full node will only accept chains that are valid according to its own local set of rules (embedded in it software), so chains of different coins will not even be considered for chain selection, regardless of the proof-of-work backing them. They just don't exists from the full node's PoV. Validity of blocks/transactions comes first, everything else is second.
