I was actually thinking about this the other day. Not only would it build upon the relationship that players have to their Sims, but it would also map out the sort of "psychology" of a Sim, and influence how they interact with the world.
I thought it would be good to have a memory system where users can choose to keep the memory or get rid of it. I think the game should auotmatically create memories, and the user should also be able to use it to create their own custom memories. I think that the current memory system isn't utilised enough and people don't even realise that it's there half the time, as is evident in the thread.
I also thought that it could work in conjunction with the traits of the Sim as well, and that instead of creating an emotional tie to the Sim, that it also creates a tie to the traits that they have and influences whether or not trait is exhibited more because of the memory or if it is downplayed due to the lack of memories concerning that particular trait. I thought that this could work by categorising the memories in generic terms like TS2, and then from there, categorising the memory into more defined terms if applicable. This would mean that traits would have to at least be able to affect this system ... So if a Sim is noncomittal but gets married, maybe the memory they have of their wedding is bad, because they aren't naturally inclined to get married or even want marriage. But this is why it would be a good idea to let the player ultimately have the final say in the memory.
The game should autonatically provide memories for Sims based on their traits. This would allow the game to have the traits be more impactful. But also so that players don't have to manually always assign memories to Sims they don't play. And it would also be good to create the option to turn memories on/off for the current household and another option to turn memories on/off for the townies, kind of like how you can do that with age.
This is tricky though, because TS4 doesn't have story progression ... so if they didn't really do anything with this feature in the first place, they probably aren't going to rework it that much.