This isn’t true. With 1559,
MINFEE would be 0 only if a plurality of miners (exact portion changes depending on how much they sacrifice, but it can be as high as over 50%) all sacrifice profits in order to drive the fee down. As long as they do this, any miner that defects from this strategy will be more profitable than miners executing the attack as long as the attack continues. When the attack is no longer executed by a sufficient portion of miners, the base fee will rise back up to its correct level.
This means that any miner that defects from the attack is rewarded, and any miner that participates in the attack is punished for as long as the attack is ongoing. Also, we can adjust the portion necessary to successfully drive the base fee down by increasing the block size target. Current EIP specifies the target as being “half full” but we could just as easily target 1/4 full which would increase the hashing power required to attack the system in this way by ~2x. The only downside of that is that we end up with bigger block size spikes and it is unclear how various client implementations will handle that so we are starting with only a 2x block size spike being possible.
Something to keep in mind is that a 1559-like fee system is sufficiently different from the system the paper is attacking that the attack no longer makes sense. Because of this, outcomes from that paper cannot be applied to a 1559-like system directly. If you want to describe an attack against a 1559-like system, you will need to fully describe a new attack.
Imagine the situation “When X = 1 and Y = 2 then X+Y = 3”. If you change X to equal 5, the conclusions that X+Y=5 no longer holds and you will need to re-evaluate things. In this case, the paper is built on the premise that fees are allocated in a very specific way, and when you remove that premise the rest of the paper no longer falls out.
Note: It is certainly possible that an outcome like the one described in that paper is possible, but I believe it would need a pretty significant rework to draw that conclusion.