On the other hand, forgetting your ideas might allow you to revisit similar ideas that you had in the past as if they were new. This could have a different and better outcome this time.
In my case, I have a very good ear for relative pitch, including chord changes and a very good memory for melody and lyrics. If I hear a song a handful of times, I can usually figure it out from memory on the guitar (although not usually in the original key).
While this is very fun in a jam session situation or at a party, it's not really great for trying to write original music. I'll start playing something that sounds nice and riffing to it, only to realize the similarity to one of the other couple of thousand songs I know how to play. I try to ignore it because I know its inevitable. Chord progressions and melodic elements are reused all the time, and many times are stylistic markers. Some bands have multiple albums that all sound the exact same. But it's not always easy to ignore the voice in your head that's like "you're playing a Coldplay song", or "you pretty much wrote this song already in high school".
Sometimes I end up trying to write around the other song, deliberately changing things to sound as unlike the song I'm trying not to rip off as possible. Sometimes that ends up sucking the energy out of the creative process. Sometimes it works.
Ultimately this isn't a one dimensional problem. Better memory is better, bad memory can help build extrapolation skills, but intention and practice can do that too. It's better to have both good memory and good inference.
I remember in math classes I would re-derive most of the trig equations on the back of every test. Meant I had to be faster at solving the problems too.
I don't think the "bad memory helps with novelty" is actually a thing. You can fall into ridged structures of thinking either way.
I can't speak to the potential benefits of good memory, since that's not something I have, but there are certain obvious downsides to having a crummy memory. One specific to the creative process is that I have a tendency to fall into particular habits, get frustrated, and forget about other techniques/approaches/tips I've read about or practiced in the past to break out of that frustration. My mental toolbox feels smaller than it should be.
I have crap episodic memory (events), adequate procedural memory (esp. for things learned long ago, but learning new vim motions is really tough, and excellent conceptual memory.
I’ve even deliberately avoided trying to remember events or how-tos in the belief they might take away from conceptual, which is what matters most to me.
I’m a cyber security guy. Conceptual is everything.
YMMV, of course.
I find that mixing both is the best path forward - put yourself in strange land, but with some solid foundation to help you.
What I have done is try to utilize the technique in the book Building a Second Brain along with the ideas from How to Take Smart Notes regarding the slipbox method.
My app of choice is Obsidian backed by a notes repo that is synced to a private git repo. This gives me access to all of my notes on any device I have.
The one issue I have not worked out exactly is how to review ideas on some frequency. I kind of feel Anki spaced repetition method does not really fit what I want to do with these free form ideas.
Anyway for what it's worth I think memory is a faculty like an arm or leg, but creativity is quite different and pertains somehow to the person's "spirit".
“a good memory aid” does what?