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.
My model is having ideas is a skill and the best way to do it is to practice at high volume. Most people are too judgemental of their ideas and they don't believe they can have ideas/having ideas isn't a mental motion that occurs to them.
If you want to have more ideas, I suggest reinforcing yourself for the behavior of having ideas regardless of their quality. A temporary delusion that any particular idea you have is REALLY GOOD is a great reinforcer. Ideally, having one idea that seems REALLY GOOD puts you in a bit of an excited, hypomanic state which triggers additional ideas.
For me, keeping a notebook of my ideas works really well. Categorizing and writing down an idea means I won't forget it and I can admire it as a new addition to my collection. I've been doing this for some years, and I now have way more interesting ideas than I know what to do with.
Another trick is to keep a notebook on your bed and write down ideas as you're falling asleep. Seems like thinking is more fluid then.
I don't ever sit down to generate ideas nowadays, I just engage in passive collection. That seems more time-efficient, because if I sit down deliberately to ideate, I waste a lot of time thinking "I don't have any ideas" and just waiting for the ideas to come. (However, if you'd prefer to do deliberate brainstorming, I'd recommend first collecting ideas for brainstorming prompts. You can make your own list: any time something makes me go "hm, that's a bit different than the way I usually think", I add it to my list of brainstorming prompts. [Note that I never actually end up using this list of prompts because passive collection means I already have an idea surplus.]) I'm now at the point where just creating a page in my notebook for "ideas of type X" seems to prompt my subconscious to gather ideas of that type. I think it's a manifestation of my internal packrat instinct... like stamp collecting, but for ideas.