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 New nodes still need to sync. Multi-TB per year will get quite unwieldy, especially as we run into physical limits to data transfer and processing speeds when we're decades into this.

Besides, you need a way to keep track of UTXOs to verify txs. Imagine when we're into the multi-deca-billions of UTXOs to track and verify. No go. 
 No you don't need to track UTXO's because UTXO's are stupid. Them and blockchain are the constraint of the whole system.

The distributed ledger is all that matters. You don't need to know "who sent what". You only need to know "who owns what". That's it. The ledger. 

The logic is simple: Has key? Has balance? Send approved. 
 What if we embed another DLT into Bitcoin as a L2? Such as a Merkel tree balance proof protocol like MINA? Bitcoin can host the top-level proof of balance, and wallets will hold branch proofs. 
 This is kind of the idea pushed even farther with MimbleWimble on things like Grin, Beam, and LitcoinMWEB