1. You will never be able to re-mine the previous block and get more fees.
The attack described in that paper consists on re-mining a block to claim less fees and incentivize other miners to continue it instead of mining in the honest chain. The threat of the opposite attack was addressed long time ago.
Since Bitcoin Core 0.11.0 (July 2015) transactions include a nLockTime to discourage fee sniping and ensure they can only be mined at a height greater than current head. Their fees can only be collected by moving forward and not by undercutting previous block. Although adoption is not widespread, you can expect it to be if this threat became credible. Also, a chain leaving less fees for the next miner will be less attractive for other miners to continue.
2. Mempool will not be shallow enough for consecutive blocks to have significantly different reward.
As demand of block space increases, or its supply decreases, it becomes more expensive. Bitcoin users will always face a trade-off between waiting a bit longer to get their transactions into blocks (until congestion subsides) and paying higher fees.
We can observe that the more transactions queued in the mempool, the higher is the price of block space and the flatter is the slope of the fee rate distribution. Thus, the lower will be the difference between contiguous block rewards. Abnormally high fees of high priority transactions published between blocks (that heap on the left of the charts) represent a smaller fraction of the total reward when the mempool is busy.
Check the clear cut at 250 sat/WU for most transactions of December 22, 2017. When fees become significantly high, many people show they are not in such a hurry for transaction confirmation after all, and you cannot expect them to be willing to pay much more for their transactions to be mined in 6 hours time instead of 7 hours.
Rewards immediately after a block is found are certainly NOT zero, "making it unprofitable for any miner to mine", as they claim.
3. Miners can always hedge undercutting risk.
Miners could include an anyone-can-spend output in their blocks, as a premium to mitigate the risk of other miners undercutting them, when their rewards are much more valuable than the fees remaining in the mempool (this can only happen if some transactions pay economically irrational amounts of fees). So, there is no need to alter transaction selection to make this possible, even in unlikely scenarios.
