so Christopher, what are you asking again?
I'm all for asking and hearing opinions and theories, even if our good ol PokeMaster specifically negated that pleasure, but your question seems a bit out of focus.
If you are asking if Red and Ash are the same person, the answer is:
*Not really, they are a different take on the experience a kid could have in the Pokémon world.*
Ash, as the anime implies, is the personification of each new generation of kids in our world.
I've noticed that lately Ash became more witty, tactical, more forefront both technically and socially.
Back when I was a kid, when Pokémon first hired, when Pichaku was still a jerk and Charmander could die from the rain, Ash was goofy, unreliable and a rather shy and sheltered kid.
This is because Ash, as I've said before, needs to evolve with the generations.
The Ash I knew is incompatible with today's youth, as my little cousin proved when I was showing him the VHS of the first episodes of the series, he found Ash to be a "sfigato" which can be translated as "stupid loser".
And looking back, I have to agree.
Today's Ash is way smarter, way cooler, both in design and attitude, he's more on the spot in comparison with his counterpart from the '90s.
Red, on the other hand, doesn't have to evolve.
If we look aside the limitations, the hardware and the gameplay, Red (as well as the other protagonists) is the same for every generations, both in the pokémon universe and in ours.
You can give Red to me, a kid from the '90s, and to a kid of today's world, and beside the kid's complaining for the technical limits of the game, we will say the same things about Red.
Red, as most other protagonists of games back then (Link is the first to come to mind), is a silent protagonist.
This is done so YOU can fill his role.
It is your team, your actions.
A good metaphor would be this:
If Ash is the bus driver, that has to adapt to new slangs, the new cool things on the block, the hots of the current generations, Red is the vehicle.
Red just needs to take you from point A to point Z, it's your choice if you want to jump down the bus and take a walk or do other crazy ***, he'll always be there, waiting for you before moving on with the adventure.*
In regards of the comparison between 'mons and Kingdom hearts, I guess that it has to do with the Shōnen genre.
In almost all the Shōnen manga, the protagonist, a young boy/ almost adult, has to surpass himself by defeating his fears/enemy etc etc, so I won't go too deeply into this, because the similarities end there.
One franchise has miniaturizable monster that can evolve and shoot beams, the other has a mix of final fantasy and disney character roster, so I don't see how those two can be relatable to each other.
But to be fair I didn't really understand your question, so I might just have wasted the last 45 minutes of my time spell checking this wall off text for nothing.