This is not really different than what we have: you can identify a "coin" as a keypair corresponding to an address with a balance, and a "non-coin" as any other keypair. I think what you are proposing would correspond to removing the "amount" from all transactions, so that every transaction has value 1, and forbidding address reuse (rather than just discouraging it). Then every address / keypair has balance either 1 (a "coin") or 0 (a "non-coin").
It would improve anonymity slightly; but people can achieve much the same benefit today by just choosing not to reuse addresses. And if they don't want to make it obvious that they have a large balance in one address, they are free to split it up, or ask people to pay them across several transactions to several addresses.
Requiring every transaction to transact 1 coin could become awkward - we've seen that cryptocurrency values can fluctuate widely. The value of 1 coin could become inconveniently small, so huge numbers of transactions would be needed to transact any significant value, causing problems with blockchain space. (Think of the Weimar Republic photos of people using a wheelbarrow full of cash to buy a loaf of bread.) Or, the value could become inconveniently large, so that most people could not afford to own 1 coin. Then you need off-chain solutions for people to own fractional shares of a single coin - this adds a lot of complexity and risk.
This is confusing. You'll need to elaborate a bit more. – Pieter Wuille – 2017-06-14T16:42:33.700
You can create an empty coin basically, and if somebody wants to send you an actual coin they will send it to your empty coin address. So there's will become empty and yours will become full. The main reason for the would be a higher level of anonymity, as addresses are often associated with people or businesses. No coins will be. – Alanay – 2017-06-14T17:08:11.013
I believe what you're really trying to say is that people should use fresh addresses to improve privacy? That's been a very common suggestion since day one. – Pieter Wuille – 2017-06-14T17:44:16.807
How do you pull together a bunch of coins you received as payments and use them to pay someone without trying all the coins together? If I receive 12 coins and pay them out as 12 coins, people will just accumulate more and more low-value coins and the system will bog down. If people consolidate coins, the benefit goes away because that ties them all together, allowing someone to tie the sender's coins together too. – David Schwartz – 2017-06-15T07:25:21.073
I don't understand what you mean, David. Coins can easily be given new pub/prvt addresses. There doesn't have to be any tracing. And why would some coins be valued lower than others? – Alanay – 2017-06-15T15:15:47.960
@Alanay, joining UTXOs (what you've been calling "coins", I think) and splitting them to different addresses is the fundamental purpose of a transaction. With this also comes a degree of traceability. If you give a value a brand new address, with no association with the previous owner, how can you prove that value came from somewhere? This is essentially creating new coins from nowhere. – Jestin – 2017-06-16T21:33:40.943
@Alanay: Your original question is still confusing. Could you please use the feedback from the commenters and the answer to clarify your question by editing it? Then we can get rid of all these comments here. – Murch – 2017-06-17T22:08:23.867