Why do you think that there are significantly fewer account values then there are unspent transactions?
Because, at least with bitcoin, you are encouraged to use a different address for every transaction. And even if you don't, each transaction still creates a transaction in the ledger with unspent outputs. If one person doesn't care as much about anonymity, they can receive 50 transactions and thus have 50 pieces of data in the log whereas an account ledger would still have 1. And when he goes to spend all that money, 50 transactions worth of outputs will need to be combined. Then those outputs could be pruned, but the intervening bandwidth usage is still heavy.
What prevents person from starting a new account each time he receives money?
Why wouldn't he do that if that improves privacy?
You can introduce some account-creation fee, of course, thus encouraging people to reuse them, but it won't be like Bitcoin at all. It's a very radical, fundamental change.
People have varying needs for privacy but bitcoin forces a square peg into a round hole, basically. An account creation fee is exactly the answer and it does not have to be expensive at all, just enough to say hey, if you want better privacy, you will have to pay a small premium. You are demanding to use more network resources, so it only makes sense. In the future when bitcoin mining rewards are low, combining transactions is going to be expensive, and you are not going to have a choice in the matter.
If you're willing to do that, you can instead force txn defrag by making only outputs in last N blocks spendable. I.e. people will be forced to send money to themselves to save it. (It has numerous advantages: it fixes "grandfather's wallet problem", prevents deflation and subsidizes fees, thus encouraging miners.)
Yeah good luck convincing bitcoin users who believe that the smallest transaction must be stored on thousands or tens of thousands of computers for all time because money is sacred and everyone should share the burden.
I believe that the right solution is 'divide and conquer', i.e. instead of having a huge-ass list of all transactions or list of all accounts we should split it into manageable parts and store on different servers. Like in a DHT, e.g. Kademlia. (Used in p2p file sharing, for example.)
With the account ledger system, assuming elliptic curve DSAs, you're looking at 100-150 bytes per account. A terabyte could hold the world's accounting.
PS - I forgot to mention that individual coins cannot be traced using an account ledger, so complex coin mixers are not required to "clean" coins.
