Your thought experiment is really very interesting. As you have stated, there are clear incentives to carry out this type of activity. Even though they are not illegal, they could represent a very effective attack vector in the not too distant future.
Perhaps the problem lies in the way power down currently works or is conceived. As far as I understand, while the user does a power down the benefits associated with the staked hive remain intact, except for a reduction of 1/14 of their voting power each week. Maintaining that benefit during the power down is, in my opinion, what opens up the possibility of this type of activity.
If we consider that the start of the power down is a public manifestation that you have decided to abandon the ecosystem, then it does not make any sense that during the power down period the user can maintain the same benefits that the rest of the community enjoys. That is, if someone decides to take the power down then their ability to continue obtaining benefits from the ecosystem should be put on hold until the power down is completed or suspended.
Of course, I understand that many users are forced to do a power down due to cases of need or emergencies, but those same users must understand that there is a price to pay when leaving the ecosystem. Typically, these users power down all of their staked hives to get a slice quickly, and then suspend it. It is very logical that these users understand that during the power down they lose some benefits.
Well, that's the conclusion I came to after thinking about it very carefully for a couple of hours, because it's certainly not a tiny problem that you've raised. In fact, you've already brought it to the fore and most likely some will be doing their math...