We have transactions fees, to avoid creating tons of transactions and increase the blockchain size to a extreme amount.
Those transactions fees are sent to the next user who is the miner.
How would the economy of a coin would change if instead of sending the transaction fee to be mined, the transaction fee was frozen and 1 year after it it would be sent back to the wallet. The user wont lose that money, but still can't keep making tons and tons of transactions to spam the blockchain.
You mean, not paying the miner in fees, only by bitcoin generation. Well, in the short term it might even work, but long term you need to pay for the transaction to be registered, so fees are kind of the motivation to keep the miners active. As of now, since a successfully mined block would anyway have a compensation in bitcoin, it could be OK, as surprising as it may seem.