Please don't judge him on out of context scenes! The Japanese version was never about that "gotta catch 'em all" mentality, that line was made up for the English franchise. "I get (catch) Pokemon!" was the Japanese tagline.
I don't like the way he captures Pokemon either, I wish the Pokemon Go influence never touched the anime, but that aside...
Unlike Paul, Goh loves his Pokemon so dearly and dislikes battling, that's why he and Scorbunny but heads at first. Scorbunny loves battling and wants to be strong. Goh, at least up until the halfway point of the series thus far (I'm still making my way through and watched some eps out of order, for transparency's sake), hates battling.
He didn't think Scorbunny should take things so seriously...
Also, Goh suffered a loss as a child that shook his trust in friendship. He made a friend called Tokio, promised to meet with him, and kept waiting outside, even bringing warm soup to keep his friend from getting cold, waiting until it was dark and it rained on him, while he waited for one of the only friends he ever made aside from Koharu/Chloe. He returned alone, miserable, soaked with rain and mud.
He thought he was lied to and made a fool of and it would be years (until current timeline) where he'd find out the truth of what happened to his friend.
He's very scared of losing friends.
He even thinks a minor disagreement with Ash cost them their friendship and asked very meekly and shyly if they could be friends again at the end of the episode.
Goh is not Paul. It's not that he doesn't care about his Pokemon, it's that he cares so deeply, but he's so scared of rejection, that his mind catastrophizes minor differences in approach and priorities and personalities and thinks "we can't be friends after all..." or "you'd be better off without me."
He's a very socially awkward child and I find that very relatable and endearing.
The show definitely should spend more time with his Pokemon, but we do rarely see them playing in the gardens of Sakuragi/Cerise labs, etc. He does train with them too, he's just more preoccupied with meeting & capturing Mew, trying to catch every Pokemon to work his way up, than in battling or training for battles. That's why it looks like he doesn't care.
It's an issue with how the show is written, rather than his character specifically, in-universe, he loves them all dearly and doesn't care much for battling or strength. He'd be better suited as a researcher or something, honestly.