This is a rare example of a problem that a (closed-membership, permissioned) blockchain is a good fit for. CT logs are already merkle trees. If a consensus component were added, entries would only be valid if the proposed new entry made sense to all parties involved.

Blockchains are fork-tolerant whereas append-only SCT logs are not, intentionally so.

You're likely referring to specific implementations of blockchains.

There is no requirement that the consensus mechanism used permit forking in a blockchain.