That's fine, even the oldest possible wallets + balances would still be in the latest output set O. We would still have the full UTXO set as we have today. I'm just saying why not simplify the really old TXs and reduce them to a hash.

Another way of putting it is, currently every node validates every block from the genesis and can see that every transaction was correctly calculated. The trust window in this case is the entire history of Bitcoin.

I'm saying, what if we could shrink the trust window to the last 30 blocks or so. Or maybe something larger like 144, but not the entire history of Bitcoin. If we can assume that there was never a period in Bitcoin's history where the entire network colluded for over 30 blocks in a row to create some false history, then a valid hash representation (or chain of hashes from the genesis) would then be good enough as a starting point.