It is my understanding that quite often people spam transactions to create full blocks, especially mining cartels with a large portion of the hashrate to force higher fees.
Your proposal might also mitigate this if there were a mechanism to instead of paying the miners for processing a negligible amount of transactions, to pay the full nodes as they are the ones incurring the costs of storing the transactions, which the fees are set up to compensate in the first place. This would democratize the rewards for supporting the network, and make it meaningless for bad actors to spam beyond the cost of storage divided by the number of active full nodes.
In an ideal world this could actually create a parity between active nodes, fee calculation, and storage cost. Would also create incentive to build a stronger node network. Would also be a major change in implementation.
This would mitigate multiple avenues of bad acting in PoW. One being the incentive to never increase blocksize, and to never engage in on chain scaling in the pursuit of massive fees. The other being the lack of incentive to spam transactions unless you are running node farms, which would likely not be profitable anyway due to a likely self blancing effect of your idea combined with mine.