Of the entities that remain, they fall into two buckets: Ones powerful enough that they already have personally identifiable data without the need to deanonymize anonymous data sets and ones small enough that they don't have the capabilities to deanonymize.
If you're a government, you don't need to rely on anonymized data sets, you have the sets with the labels already. If you're a stalker or internet troll or whatever, it's far easier to just pay one of the PI websites $29 to get far more data on a person than any deanonymized dataset will give you.
So, I would imagine everyone becomes more powerful over time.