Almost every property has different licensing rules & restrictions. I had to deal with this quite a bit in the video-game industry.
For example, for STTNG when we licensed the property, we got access/permission for all the (current) main cast. However, they still individually had image approval - for wherever their likeness was shown. Some of them were picky about it, others were like "whatever". Using an image of the whole cast was hard, because there were very few instances where ALL of them were okay with it. Williams also got several of them to do custom voice work - this certainly cost extra above the regular license fees.
As another example, when we licensed Mission:Impossible, we were not given permission for Tom Cruise's likeness (even though he was involved), but we could use "Ethan Hunt" (it had to be a "generic" looking Ethan Hunt). We did have permission for other characters & actor's likenesses (and got voice work done from a couple).
And these were both Paramount Pictures licenses.
Who knows what the details of the Addams Family license (from 30 years ago) would include or not include. It's possible it wouldn't be that hard, it also could be impossible. It also could be done with some work-arounds (i.e. modifying the art/sound to have a "generic" Gomez if Raul Julia's estate objects).