I'm not sure who misunderstands. I'll try to rephrase.
Here's the core of my question - does the system (all nodes) forget a prefix of the chain at some point?
If a node reads the entire chain (from genesis), it can prune it locally, sure. But how does a new node bootstrap without the entire chain? It needs to trust a snapshot (rolling root, utxo block, whatever it's called). That's my issue.
Rolling root and UTXO are very different architecturally, so I'll just answer for UTXO here.
Nobody, whether it's new nodes or old nodes, needs to know the entire histories of coins. The only thing that matters is whether they have the accurate unspent transactions.
New nodes download the entire UTXO meta chain (step #2 in the summary I posted earlier). This chain is protected by PoW. That's it. By knowing the accurate UTXO tree fingerprint, they can safely build the UTXO tree.
No offense, but I'm not sure you understand "UTXO" well enough to explain it to others. For starters, UTXO is nothing new, this post is about "committed utxo".
As maaku explained, miners need to know that they're mining on top of the valid chain, that's the only way they can know they have the accurate UTXO.
I don't think validity of commitment touches validity of Bitcoin block. Bitcoin nodes are allowed to completely ignore this merge-mined chain.
There's two ways to implement this: as a merged mined chain or as a softfork. The soft fork would invalidate blocks with an invalid utxo root, with the merged mined chain their validity is independent. I prefer the second option, the mini-chain just seems like a mechanism to deploy it, but until you make the soft fork this is not that useful.
Then these Bitcoin nodes (aka Bitcoin) should not truncate the chain. When you truncate up to some point you trust that you have a valid snapshot up to this time. There is no way to verify the UTXO chain (in the sense that there can be missing transactions) once the prefix is gone. So if someone manages to slip an invalid utxo into the blockchain, and this error is discovered after the prefix is gone, it invalidates every node that forgets prefixes.
So it could work as a fast-bootstrapping probably-reliable mechanism for your home PC. Something between SPV and full wallet. But to be done in full nodes the snapshot mechanism has to be incorporated in the blockchain.
Not sure what you mean by "prefix" here, it seems you mean the past chain.
With committed utxo SPV nodes can be much more secure, but full nodes still need to fully validate the chain (otherwise they would have SPV security, not full node security).