Thanks for the explanation. Seems to be an interesting idea to hear. But going by your idea, I don't think this could work in real world. Not all miners use the coins for transactions, there may be a lot of them who hold the coins for long term. Holding for a long term is equivalent to not indulging themselves in any transactions which makes them according to the network the least possibility of becoming a miner.
They don't indulge themselves in transactions because they don't need to here he would need.
There even an already existing case, called proof of burn, where people send coins to a wallet X and the total amount of coins they ever sent there are their stake. From the point of view of "I wont spend my coins because I am a miner" this is even worse, because at least, at proof of transaction fees, the transaction fee has a dual purpose (work as a normal transaction fee too).
For instance, a miner named A is one of the biggest miners in the PoW period of the coin. He didn't spend the coins and would like to hold the coins for longer term. Once the coin shifts from PoW to PoTF algorithm, the network searches for the miner with highest transaction fees, sadly he won't be chosen by the network but he wishes to mine the coin and be a helpful member of the community.
I think I see what you are talking about, at least with POS, to mine POS the user need to not spend his money during the period he want to mine, but to then be able to mine when proof of transaction fees era start, he would need to have money spend with transaction fees. Some would not want to mine with stake because if they do, their wont be able to spend their money at transaction fees and have less "Mining power" at start of proof of transaction fees part.
Well, one thing those guys could do is just spend all those not spent money with transactions fees while doing an transaction fees to an alternative wallet they have, they would by doing that, "get their mining power back".