I am playing Pokémon gen 1 via a romhack, PureRGB, which is like an enhancement that tries to retain the feel of Gen 1 (whatever that means). Finally, Pokémon Green is tolerable to play!
But anyway I was thinking about the two main characters and how I think Blue is a good rival not because he's a brat but because he's a good foil to Red. Blue is loud, outspoken, brash, bold, and yeah a brat. Red is outgoing in a different way, he is silent, he does things at a moderate pace and whatever he pleases.
And I also think based on how Gen 2 ends, he is not social/antisocial. I think he probably only connects with Pokémon, and this is the real reason he goes out of his way to stop Team Rocket. Think about it; nobody actually tells him to do any of that. No champion is driving him to do so, or pushing him to that path. Obviously you have to beat TR to progress, but narratively, why did he do any of that? Because TR is cruel to Pokémon and he loves Pokémon.
Back to Gen 2, I think that him ending up alone on Mt. Silver is a pretty natural conclusion for someone who doesn't jive that well in human society. Isolated, only his monsters to keep him company, hardly speaks to his own mother. It's cool as a gameplay moment but when I think about it, it's a little sad but understandable. At least he seems to be on good terms with his childhood friend in Gen 7.
(All of this also applies to Leaf, if you so desire.)
I also think Blue's conclusion is fitting. He gets humbled by his rival, and his retrospecting on what happened to Cinnabar Island parallels his short lived championship, I think. Also, he becomes a Gym Leader, which you can consider a mentor of sorts. Showing trainers like who whe was how to become better.

