But I am not suggesting for it to be exchanged for money, but rather just pairing it with another blinded coin made from thin air, comitted by the receiver of the transaction, together with the proof. So we will not have any addresses ever, just pairing of committed secret serial numbers with the proofs in between. Let's say we have miner generated coins Mc1-Mc3 in the first 3 blocks. Then miner 3 wants to transact his coin over to user 1 (non miner). User 1 makes a coin Uc1, just like the miners, and sends it to miner 3. Miner 3 then pairs this with his own proof Mp3 and publishes it to be taken from some random other (here miner 1). Then you have the following after block 4 (who is registering the transaction):

Mc1-(Mp3-Uc1)
Mc2
Mc3
Mc4

Miner 3 can´t re-use his proof, so he has not got his coin anymore. The other 3 miners have yet to publish their proofs, beside User 1. So still only 4 coins in circulation.