So today I had a random thought. I look back and I think to myself "What made Red and Blue Versions more enjoyable to me than the later ones? And I came up with a few conclusions that I just wanted to incoherently ramble about.
Maybe it's just because I was a lot younger back then and susceptible to such things, but Pokemon Red and Blue Versions feel more like "This is you. You are starting your adventure." Whereas later games feel more like you're playing as a character and guiding THEM on THEIR adventure. This is part of the reason why I've started playing as the female characters in these games (That and Lucas's stupid hat).
But with R/B the character design is fairly minimalist, the story is pretty minimal, so it feels more like it's just your daily life in the Pokemon world. Later games have complex plots involving saving the world from total destruction, but back then the villainous team was more relatable to real life. They were just a criminal gang whose main goal in life is to make a profit through nafarious means. So it feels less like you're a hero, and just an upstanding citizen doing what's right.
Then of course there's Cubone. When you find out that the Team Rocket killed its mother, it's... real. There's no other way to describe it. It's not cartoony and over the top in any way, like when Team Galactic bombed the lake and you have to navigate the dry lake with dozens of Magikarp flopping around you. It's one of those things that can easily be applied to real life tragedies, especially if they involve gang related violence.
Even the Pokemon themselves seemed realistic in their sprites. Their sprite designs are a lot less cartoony than in recent games. You look at Kakuna and you think "That is a creepy bug." just as you would any creepy bug in real life. Even newer designs of Pokemon tend to be colorful and cartoony enough to make one think "It's a character akin to Mario and Sonic." Rather than the real life big catching adventure the series was inspired by.
Even legendary pokemon don't seem as natural nowadays. Many of them are given a context and backstory that you hear about well before you encounter them. But back in the old days? You're walking through the ruins of a power plant and THIS BIG SUPER POWER LIGHTNING BIRD OUT OF NOWHERE WHAT THE HECK IS THAT!?
It feels like a phenomenon, like you're walking through the forest and all of a sudden a Sasquatch appears before you.
Then of course there's the nostalgia and general fact that they were the first time we'd ever gone on such an adventure. By the tenth time you play a Pokemon game you already know so much of what to do and how the world works. You see a Bellsprout and you're immediately aware that it can do stuff like wrap and sleep powder, especially if you study its movesets beforehand.
Of course back in the day you couldn't see what moves a pokemon learned or how strong said moves were. It was all a giant gamble. You can't just pick up a ferret and say "This little guy will learn to Bite in two weeks. It'll be this strong."
I want to say NPC roadblocks were less contrived back then, but we never did find out why the thirsty guards are blocking the path to Saffron. Maybe they were bribed/threatened by Team Rocket? At least it's not just a bunch of people dancing for no reason who claim they'll disappear some day, for no reason.
And of course for those of us like me, age is a factor. I think I was around 13 when I got my first copy of Blue Version, and the protagonist was a ten year old. Not far off but still you can fit yourself in that position, especially with the minimalist sprites and design for the player.
Now that I'm easily older than most of the gym leaders in these games it doesn't feel quite the same. It doesn't have that feeling of being immersed in a strange new world, set on a journey of growth and self-discovery. It's more like playing a Mario game. Maybe you can relate to Mario, but he's clearly his own character.
And thus concludes this utter nonsense I typed out while woozy and exhausted from yard work. So yea, nostalgia is a factor.