But for the sake of a tiny increase in trust, you get a network where new full nodes can be brought online without having to download several hundred terabytes of data. EDIT: that still retain their ability to verify all the way back to the root, on their own time.
Satoshi already created a 100% trustless solution to this called SPV. It allows lite nodes to be instantly online and download from peers only the portions of the blockchain they need in real time. Install client and you are instantly ready to start transacting. Your "solution" doesn't work but even if it did would be inferior to SPV which is something Satoshi came up with before the blockhain even started.
You see, as I've mentioned, I have read the Bitcoin paper. Several times. I understand it well.
No you don't or you wouldn't make mistakes like saying "transactions which are spent" or the one you just repeated below. You also would have realized the SPV clients exist.
The Bitcoin paper points out this interesting property of the blockchain: that the longer it gets, the harder it gets to fake. Impossibly harder.
This isn't in a vacuum that property only applies because for a given tx, the tx, and everything that is needed to validate that tx is also deeper in the blockchain. You can't throw that away and then assume the same dynamic is in play.
The relationship indeed becomes no longer 100% trustless as I've acknowledged multiple times.
Any system which is not 100% trustless is inferior to the system we have now. Why would you want to make the protocol worse. The only way space ever becomes a concern is if Bitcoin becomes many magnitudes larger which means an economy valued in the hundreds of billions if not trillions. Any amount of trust when the payoff is that large will be at risk of compromise.
If Bitcoin gets to that point, you will come back to this proposal, and you will see it in a different light all of a sudden.
If Bitcoin "gets to that point" true proposals for a ledger system will be given more weight but true proposals actually address the risks rather than just pretend they don't exist. You haven't proposed anything other than drop all method of verifiy a transaction, throw it into a new block at the head of the chain and hope nobody abuses that. That isn't a proposal, that is nonsense.
Pruning is very likely to keep the storage requirements modest. It is likely Bitcoin will never need a ledger snapshot system but if it did it would require more thought that what you propose. Still the true bottlenecks to transaction volume are node bandwidth and memory. You are trying to "fix" the bottleneck which isn't a bottleneck while consuming resources on the actual bottleneck.