The encrypted list is stored on the devices for security and performance reasons: otherwise it would be too easy to ship people customized lists with arbitrary images. You can't just rapidly revise the list without undermining the privacy protection here.
Also the space of modifications is gigantic, for any given image there should be millions of differently hash variations which can be reached without major visual damage. (at least for neuralhash the figure is billions)... so you can't just stick all of them in the database.
You could stick widely circulating variations in the database, however... sure.