@neo wrote in the recent topic Analyzing the Google Attack
This is what I was asking about, when it came to double-spending coins, and so on.
If a coin file will contain a history of valid transactions, however, at least every honest recipient can check it for themselves and eliminate the possibility of the coin suddenly appearing in someone’s hands. What that means is that every holder of a coin can know that no one will “steal” the coins from them, even if an attacker takes over the consensus of an entire section. Yes, dishonest recipients might still “accept” payment, but they’d only be screwing themselves, because they can’t forge an invalid history without also controlling the devices of some earlier recipients of the coin (i.e. their actual client devices to sign the coin away, which makes things much harder even than before), so recipients down the line won’t accept their token.
So I think it’s a worthwhile addition, to improve the safety of the coins.
PS: However, it is true that if an attacker is able to control at least one of the previous recipients A, and make the network forget that A signed away the coin (e.g. by sabotaging that section) then they’ll be able to double-spend it. It could be A themselves, who let a very valuable set of coins pass through them and then do it. So, to recover, the network should accept proofs that some other fork happened earlier, but this requires the Permissionless Timestamping Network to be added, which might be too much work