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.
It's one thing for it to be frozen and a different thing to have the fee returned, it would simply clog the whole chain for a year if the returning fees would have their own space in a block.
The user wont lose that money, but still can't keep making tons and tons of transactions to spam the blockchain.
Actually no, it will not prevent them from doing so and it will only make sure he can repeat this thing every year at zero costs.
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.
This makes zero sense.
PoB is an alternative to PoS, and furthermore an algorithm that has never been successfully tested with any coin, and it's far easier to attack than PoS, let's compare the number of people who will stake coins for a reward and to protect the network and the ones willing to burn their money for it.
Oh, and in the end, nothing is being solved.