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.