Just an opinion: ideas do not come from nothing, so the larger the data pool (memories, experiences, interests) the more ideas are likely to be generated.
It very much seems like we live in an age of hyperspecialization; people know very much about relatively few things. Generally, these areas of knowledge are complimentary or related. Sometimes they overlap outright. Life is barely long enough to get good at one thing, so people often choose to specialize early and stay on one very fixed path.
From the outside looking in these collectives of experience are very tribal. They develop their own languages and symbols. They become these closed systems where ideas aren't created as much as they are simply refined; bounced back and forth among tribal members. But this does not seem to be a very good pattern for long term growth or sustainability. Homogenization leads to extinction.
What I mean by that can be understood by looking at the evolution of life on Earth as an example of the obverse. Evolution tends towards diversity. Diversity gives life its best possible chance of success. That way, when an asteroid slams into the planet, not everything dies. If evolution had tended towards homogenization (only making the best dinosaurs possible) instead of diversity, the K-T Event might have turned this planet into a floating rock.
It may be a bit of a weak analogy, but I feel like the same principles might apply fairly well to specific areas of knowledge. Ideas are the mutations that allow knowledge to change and evolve into something new. Exclusivity and specialization are a sort of homogenization that leads to stagnation and fewer truly new & good ideas. Not that ideas don't happen at all, just that maybe they happen less often than they should... or could. I don't know, really. This is mostly just speculation based on personal observation and opinion.
Colloquially, I can say that the people I have known in my life who seem to have the most ideas are the ones whose interests are all over the map, so to speak. They tend to be older, with a deeper well of experience to draw from. Their knowledge pools, being varied as opposed to complimentary, allow them to look outside these otherwise closed systems and make inferences, or to see patterns that people too mired within the subject matter might easily miss.
They may not always be good ideas, but they are often striking in their seeming originality and unexpectedness.
An example that comes to mind is of a family friend who worked for years in automotive manufacturing before going back to school to get his certification as a laboratory technician. He got a job as a lab assistant at a University research hospital. He would overhear the researchers in the break room talking about their current projects, and one of them that really grabbed his interest was the problem of infectious disease control measures, specifically, getting healthcare professionals to wash their hands between patient interactions. He had the idea, based on his experience in manufacturing, to apply Poka Yoke (a Japanese manufacturing term that roughly means error-proofing) to the problem of getting nurses and doctors to wash their hands between patient encounters. His idea was to install sink-locks at all the doors to patient rooms. These doors would only open from the outside if the sink was used for at least 20 seconds immediately prior to opening them, or if an emergency button was pushed. From the inside they open at will. He mentioned the idea in casual conversation with one of the senior researchers who was so excited by it that he wanted to design a study around the concept.
I feel like there is a potential benefit to be had by looking outside as opposed to focusing too intently within. Maybe spending some percentage of time learning about completely new things as opposed to only endeavoring to learn new details about things we already know might yield an increase in new ideas. There's nothing wrong with getting out of our comfort zone and challenging our perspectives.
I believe for some people it's very important to have a moment of realization that one can get to the frontier of knowledge in a given field of interest. It feels intimidating if others are making contributions that seem decisively out of your league. Because people might intuitively underestimate how far you can get with focused reading and learning, it could be good to give tailored advice to people newer to (e.g.) AI risk for how/where they can make contributions that will feel encouraging. For illustration, a few years ago I was playing a computer game for fun for quite a while until I was by chance matched up with the one of the better competitive players and I almost won against them, getting lucky. That experience showed me that I'd have a shot if I actually tried, and it encouraged me to immediately start practicing with the aim of becoming competitive at that game. It changed my mindset over night. Similarly, I think there's a difference in mindset between "reading and talking about research topics for fun" and "reading and talking about research topics with the intent of seriously contributing".
I agree with others that a rewarding social environment and people in a similar range of competence you can bounce ideas back-and-forth with are extremely important. If you collaborate with people who are similarly driven to figure things out and discuss ideas with you, that automatically forces you think about your ideas for much longer and in more detail. By yourself you might stop thinking about a topic once you reach a roadblock, but if every morning you wake up to new messages by a collaborator adding criticism or new bits to your thinking, you're going to keep working on the topic.
I also suspect that people are sometimes too modest (or in the wrong mindset) to develop the habit of "taking stances". Some people know about a lot of different considerations and can tell you in detail what others have written, but they don't invest effort coming up with their own opinion – presumably because they don't consider themselves to be experts. Some of the community norms about not being overconfident might contribute to this failure mode, but the two things are distinct because people can try practicing taking stances with personal "pre-Aumann opinions", which they are free to largely ignore when deferring to the experts for an all-things-considered judgment.
Speculation about personality traits conducive to generating ideas: OCD was mentioned in the comments. There's also OCPD and hyperfocus. Carl Shulman's advice for researchers among other things mentions something about having a strong emotional reaction to people being wrong on the internet (in communities you care about) – I think this might be a symptom of being very invested in the ideas, and it can help further clarify one's thinking while trying to articulate fervently why something is wrong. Need for closure also seems relevant to me. It has its dangers because it can lead to one-sided thinking. But in me at least I'm often driven by feeling deeply unsatisfied with not having answers to questions that seem strategically important. And, anecdotally, I know some people with low need for closure who I consider to be phenomenal researchers in most important respects, but these people are less creative than I would be with their skills and backgrounds, and their obsessive focus maybe goes into greater width of research rather than zooming in on making progress on the "construction sites". Finally, I strongly agree with John Maxwell's point that a "temporary delusion" for thinking that one's ideas are really good is a great reinforcement mechanism (even though it often leads to embarrassment later on).
Re temporary delusion that one’s ideas are important (or new): a good example is individuals who file patents. They think they have a world-beating invention. In fact 90% of patents are never used, and getting a patent costs a fortune. There’s a well-known phenomenon I’ve heard called ‘search shock’, when a naive inventor goes to a patent attorney, who conducts a patent search and reveals to the incredulous inventor that every supposedly original, brilliant aspect of the invention has been both thought of and patented before.