I always thought of Memory as being analogous to the Thrill, more of a "cultural" ability related to the epoch kingdoms or even perhaps "spiritual dna". From Dalinar's first vision (ch 19 I believe) where he spoke with the Radiants we learned each of the 10 epoch kingdoms had a specific purpose to help against the Desolations. The purpose of the Alethi was to be the warriors, so my theory is the Thrill is something that they gained in order to improve their combat skills. Giving one kingdom Memory also makes sense: they can remember something perfectly until they transcribe it and thereby pass down knowledge to help future generations against Desolations. Shallan does this through art, but I wouldn't be surprised if she could keep an entire event as a Memory and write it down.
I'm not saying that everyone in Jah Keved would necessary have this, at this point we haven't met enough people from Jah Keved or enough about Memory. However, hair color is indicated as a trait of pure ancestry for the Alethi, the more black the more pure (it's even noted that the nobility has less dark hair because of their need to marry foreigners for strategic purposes). Shallan is described early on as having red hair which is an oddity and causes her to stand out. If these abilities are genetic (spiritual or physical) it could be something that has been lost over the years through intermarriage and Shallan just happened to get the traits for it. It could also be an ability from another culture entirely.
The idea that each of the 10 epoch kingdoms had a cultural trait outside of the Radiants that would help them through the Desolations makes a certain deal of sense to me. Particularly if those kingdoms became extremely specialized. We just haven't seen enough of them yet as so far every main viewpoint character we have seen is Alethi except Shallan.
Also so far all the powers we have seen related to the Radiants/Soulcasting involved the use of Stormlight and sometimes specific types of gems. I don't recall anything from the books where Shallan needed Stormlight or a type of gem to create a Memory.
Side theory: abilities such as Thrill and Memory are related to a person's Calling. The Calling in the book sounded like it was something you could pick and then later change, but based on Kaladin and how he feels whenever he picks up a weapon it could also be something baser.