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.
The transaction fees are the part that should ensure Bitcoin run forever. The block rewards are decreasing, rather sharply. When those will become really small, the miner have to be paid somehow for their work. That's what the transaction are fees for, not only to avoid network spam.
This being said, if your idea would be implemented, in some (many?) years from now, there's a (good) chance the miners will leave.
Yes, I forgot about that obvious part. It would require changing the system.
Some examples of those changes would be
Proof of burn that after X months send the the coins back to be rewarded to the miner and mining is based at amount of coins you burned and were not sent back to the miners yet.
Proof of burn that instead of going to a unspendable wallet, it is added to reward (money would be based at all money you used).
You can select if a transaction fee will go back to you after 1 year or will be back to be back as reward. The amount of your transactions fees that came back as reward is used as stake to find the one that will be the miner.
Same as previous but if you select to make the transaction fee to back to miners as reward, it will happen instantly at next block.