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 fees are an incentive to the miners to propagate and secure the network in a decentralized manner. If you remove the profit incentive from miners by returning fees to the transactors, there essentially is no reason for anyone to spend resources on propagating the network. The result is a less robust and less secure network, and if the network can't be trusted to be secure, the price of the crypto suffers because no one is going to spend a significant amount of money on an asset that might prove open to manipulation.
As I explained before, you could also allow users to send coins to some place that will be given back miners as fee, but this would require replacing proof of work with that (or using it together with proof of work).