In my opinion, the reason why Goh's character is fleshed out that way is because honestly if there's nobody who's out to catch them all at this point it would be really hard to integrate all of the Pokémon so far into the anime into a seamless, plausible plot. Goh has the most Pokémon, yes, but many of those will have that most screentime and attention with that than they have had and could have had.
Because of that, it's highly unlikely that Goh will make it into the next series. Why? It's because he's probably going to catch most, if not all, of the regular Pokémon by the end of this series. If he's going to do it again in the next one, it'll be pretty redundant. On the other hand, his character is pretty much set on the catcher archetype, and him doing otherwise would be less logical than say create a new character.
My bet is by the end of the series he's going to say there's more to catch and that Mew is somewhere in this wide wide world of sports and continue on his search alone.
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Now in my opinion the reason why there is so much discussion about the carry over of characters is because of one and only reason alone.
Brock.
Brock has been one of the longest running characters appearing for 3.5 seasons and in 4 regions. Other than Ash himself and Team Rocket, he's got the third longest resume in the show.
The reason why he lasted that long is because Ash needed a mentor character until Generation 4. Brock could have continued in Generation 5 (and personally, I wish he did), but if he did they wouldn't be able to do a reboot of Ash's persona and knowledge since Brock has been with him and seen him in his peak condition in Sinnoh. So they replaced Brock with Cillan, who is a mentor-ish but also gives more leeway and sometimes appreciative of Ash's childish behavior in Unnova.
After that Ash has become the bonafide leader of the team in Gen 6 or 7. There is no need for another person to be the "wise man who holds knowledge from journeys past" because Ash already is that person.
That's why going forward we're probably not going to see another character join him from region to region. Goh is probably the most equal of Ash's newest companions, but we also know that Ash is still really the one who will get the job done. As such, even if he will be brought to a new region, Goh's still going to act the same and not really add anything new, making him redundant with any new character.