A good Pokémon game should also be a good JRPG. Now obviously there are some differences when comparing Pokémon to a JRPG, like the level of story focus. However, you should look at Red and Green as the quintessential Pokémon experience. Ignore the anime, ignore remakes, ignore manga, ignore your preconceived notions and look at the beginning. What is the aesthetic? What is the feeling? What is the purpose?
You're a boy with a best friend/rival. The movie playing as you leave is Stand By Me, this is a personal journey. You're tasked with filling the Pokédex, but you also decide to face Gyms and work your way to the League. There is a competitive drive between you and your rival as you intercept each other multiple times across your journey. Your evolving teams mimic your own growth. You scour the lands, backtracking to find rare monsters. There are even powerful monsters said to be legendary in nature. It's your journey, a "boy's summer" as described by Ken Sugimori. In real life, the rare monsters you and others find encourage interaction through trading. But you see a lot of the childhoods of Game Freak manifested in early Pokémon, from kaiju to tokusatsu to collecting bugs. A good Pokémon game will always have this as its core, and it will focus on being more, being better than the last by adding new content (ie. Gym Leader rematches) and new ways of exploring the world to find new Pokémon (ie. Mach/Acro Bikes). It's your journey, your story, and your agency matters.