This chart brings up a very good point. Like you point out, in such a scenario, the miner can only earn a profit if he can include a sufficient number of fee-paying TXs in his block. But what happens if the miner before him cleaned out the mempool? It seems the rational miner will stop hashing1 entirely until enough new transactions have built up to push his block into the "profitable" zone in your graph (the zone where the supply curve is below the demand curve).
Do you see this as a problem? I see this as the network working at its maximum efficiency... note that every miner will have a slightly different cost so hashing power will turn off at different times. And if running intermittent hashing power causes blocks to come less often than once per 10minutes, the difficulty will be reduced. The reduction in difficulty will allow blocks to be found with less hash power so your hardware will be more likely to find the block. This means miners will power up their hardware with fewer transactions in the mempool.
So the system self-adjusts.
The awesome part of it is that there is NO minimum fee. Difficulty will always adjust to allow the minimum fee to be whatever people are willing to pay (presumably to just below competitive money transmission systems).
No, I see this as a positive. I agree with everything you wrote above.
However, one thing I'd like to reconcile is the fact that Eq. (11)
suggests the cost to spam the blockchain falls to zero as R->0. I was wondering if my model "breaks" when the block reward becomes small because it is not considering that rational miners would stop and start hashing depending on the fees available from mempool.