Imagine Alice owns 10 BTC and wants to send 1 BTC to bob, with a 1 BTC miners fee.
In the blockchain, the transaction is recorded as "Alice spent 10 bitcoins, 1 goes to Bob, 1 goes to the miner, and 8 goes to Alice".
That seems rather unintuitive. Why not just record the payment and miners fee explicitly?
I've looked into this before, and I've never been able to find an explicit rationale from Satoshi, but there are a couple of possible reasons.
Imagine that rather than using the spent/unspent model, you track the balance of each address. You get a zero-confirmation transaction that pays to you from an address.
Now, to figure out what the balance of this address is, you need to get all of the deposits and withdrawals from it. If you miss one, you calculate the wrong balance.
You could fix that by forcing each transaction from an address to reference the last transaction by hash, but that eliminates an important property of Bitcoin - multiple deposits and withdrawals to and from the same address can be processed at the same time, without coordination between them.
The change output (which you referenced as '8 BTC goes to Alice') is sent to an entirely new address, and in theory it is not possible to figure out which output is the change output. In practice, the real output is usually a nice round number, and the change output is something like 0.00019841.
If you've used Bitcoin for long enough, you've probably run into a situation where someone sent you some Bitcoins, but didn't attach a fee.
If the change output were explicitly marked, the sender could just resend the transaction with a slightly smaller change output, and a slightly larger fee. Miners would know that they could safely accept the new transaction into their memory pool without helping anyone commit fraud. Then, we wouldn't need stuff like replace-by-fee or child-pays-for-parent.
If you have 50 outputs that make up your money, that means that you're taking up 50 times more space than you would if you had a single balance.
TL;DR: It could have been done differently, and there are some reasonably compelling arguments, but it's impossible to change now.
Transaction outputs only have two states, spent and unspent, so spending part of one is not possible without the creation of another. With a boolean spent/unspent there is no state to have to store and recall, which allows for simpler states in wallets and makes scaling away from the block chain significantly easier. Imagine if we had a transaction spending a decrementing amount in an output, what's to stop that transaction just being repeated and debiting the amount again? Having atomic outputs means you don't need to worry about things like serial numbers, which alternate systems like Ethereum and NXT do, due to their lack of inherent replay protection.
There's additionally no purpose in stating the fee if it can be inferred, and doing so saves space in the transaction.
Transaction outputs only have two states, spent and unspent, I understand that. I don't understand the reason for designing the protocol that way. Why was this system chosen?