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 business model of the crypto mining industry would shift to adapt.
Miners would seek ways to consistently and reliably profit from holding transaction fees for 12 months. There would be an additional abstraction layer added where miners would try to earn 100% interest on transaction fees in 1 year. To enable them to profit from fee holdings, so that they could essentially keep it.
In a way, what you're describing is a financial perpetual motion machine. Which continues to operate reliably and efficiency on a near -something for nothing- model of energy/capital.
Its commonly said that people get what they pay for and reducing transaction fees in this way, could result in reduced hash rate, performance and reliability.