I think here you misunderstood. My "variation" of the proposal means that there should be fee competition. If the space where such redeem transactions can be included is limited, then transactions will compete for this space. Even if the block space was unlimited then the users would include a fee because otherwise no miners would include their transactions. But with a limited space there can be situations where the competition leads to a significant income for miners.

As the OP wrote, these transactions are "free money" for the miners, so they will include them even if the fee is very low. On most altcoins where the fee competition is low (e.g. LTC) it works in the same way.