Anyways, to really understand what happens when R->0 I think we need to make a new model that takes into account what we just learned from your chart above (that miners won't necessarily be hashing all the time).
That seems to be an interesting point illustrating how the best interest of users and miners incentives could diverge.
For users, an empty block is always better than no block because it adds work to the chain and increases the security of the previous transactions.
"interest of users and miner's incentives could diverge"... this is a very odd way of describing the situation because these interests are of course divergent.
The interest of a seller is always to sell at the highest price, and the buyer to buy at the lowest. It is this tension that makes price discovery work.
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).