Checkpoints in POS (and to a lesser extent in bitcoin) add trust to the equation. You might ask if checkpoints are so great, why not have them for every single block and the obvious answer is that this means you are trusting the checkpoint producer 100%, which is against all that trustless crypto attempts to achieve.
LCR should mean that you don't need checkpoints at all; this is something which POW has over POS and all other consensus techniques which do not expend a resource to create a block.
I agree that checkpoints in POW fail the trustlessness goal. It seems you also agree that POW/POS are never both append-only and trustless. But based on my reading of the consensus algo of eMunie, its possible to have a ledger system that is all three important qualities: trustless, append-only, and resourceless (meaning doesn't waste resources). Is there another crypto with those three?