1. Introduce mechanic that kids or older people with retained inner childhood can relate to: i.e. catching critters and/or maintaining a collection.
Kids go outside, find something curious, oftentimes a bug or a frog, etc. That can occupy their attention to no end. Convert that to Pokemon standards. Kids or even older people collect toys, stamps, bottle caps, figurines, antique cars, you name it. It becomes an obsession. You want to build your collection as much as you can. Convert that to Pokemon standards.
All check. You grabbed their attention and tapped into their favorite hobbies.
2. Make everything aesthetically pleasing. What do kids or individuals with vivid imaginations like to look at? Cute furry animals, cool looking dinosaurs or reptiles, flashy flying creatures (birds, bugs, mythical monsters, etc.). Cover as many bases as possible to appeal to a wider audience.
Check. You make them feel comfortable giving you their attention.
3. Maintain Step 1. Rinse and repeat Step 2. While 1 and 2 are still stable, incorporate some form of storytelling to build the world. Give them a reason to share their collections and compete with others like them. Competition breeds the desire to improve. This makes people go back to play and build on what they already know. Competition also breeds the bandwagoning effect. If you're successful, others want what you have. This causes people to also compete for information and resources, thereby giving the franchise the spreading wildfire they need.
4. Bonus: repeatedly market to veterans or "power users" who are experienced with your content since the beginning. These are individuals who act as your brand ambassadors without them even knowing it. They're the ones who tell their friends, their family members, their kids (if they have) about an old passion. They're the ones who are uniquely influenced by the brand, due to a combination of nostalgia (inner childhood; see Step 1), the desire to be intrigued and the desire to build (again, see Step 1).
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How often do you see people (fans, professionals, random onlookers) criticize the repetitiveness of Pokemon? We all know they follow the same formula. You give people a vehicle to collect something and actively build upon that collection. You give people the opportunity to use said collection to compete with other people's collections.
How often do you see people criticize Pokemon designs? Villainous team outfits, despite their constant rehashes? That's because it is critical for the franchise to have assets that are aesthetically pleasing to as wide an audience as possible. As soon as a larger number of people lean toward the "WTF is that?" mentality over the "That's pretty cool/cute/interesting looking," you're going to start a downward spiral, lose trust, lose fans, lose momentum.
And speaking of momentum, you don't stop, and Pokemon as a franchise does a fantastic job with that. Even in the earlier days, they relied heavily on advertising and relentless pushes of new merchandise. It was the game and the cards, soon followed by the anime. Using Pokemon Yellow to capitalize on the anime while it was still the hot thing was a genius move. Pumping out a steady dose of movies further boosted the brand image.
Even as one aspect slows down in terms of hype or interest, there are so many other weapons in the arsenal by that time that the franchise can afford to reallocate resources to capitalize on what's currently trending the most at the time.
Did you notice how Pokemon has taken a bigger step toward incorporating really heavy-fantasy storytelling in the core games? Many people raved about the story aspect of Black and White and see what happened in XY? They continued the trend. In ORAS they pushed out the Delta Episode considering the remake of the Gen III storyline could not give them the room to be flexible. It'll be no surprise that "Z" would likely be story-driven as well. Note I never mentioned story quality because that's subjective.
So that's what's working for them now. But because they're culturally significant at this point, they have the luxury of reusing the same formula until it no longer works. And because after nearly 20 years people still pile onto the same merchandise year in and year out, Pokemon can continue thriving. Other companies either abandon the working formula in favor of experimentation, only to outright fail or disconnect themselves from existing fans.
Why do I stick around? I'm in Step 4 as I listed above. I've been with the franchise literally since the beginning. I've lived through that original "Pokemon phenomena" that took the world by storm. It's a combination of nostalgia, curiosity in global cultures, and a genuine interest in the gaming industry as a whole.