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).
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".