Gonna be honest. I don't understand why Morty even give a shit about going back to C137 at this point. Ignoring everything else, He's gotten more action with Jessica in the new dimension than possibly every other Morty in the multiverse except maybe Nazi Morty.
It's not clear that the Morty we're following is C137, as it's never stated in either game.
As to Morty's attitude about going home, that's more complicated. Remember that this version is a remake of the Unity game, a game that is still in progress, and that I have no input on or future knowledge about. I can make small deviations, minor dialogue changes, add on to some scenes, things like that, but since I don't know where the story is going to go, I need to be more mindful of radical plot alterations.
For example, making Morticia be more like a twin sister, that's just a name change. It's minor enough that I was able to make it a selectable option. Or letting the player define Morty's age, again, fun extra with no real story impact.
I've also made some medium changes, like how in the Unity game, Morty thinks of his mom as "Beth" and not his real mom. Where as in the renpy version, he just calls her mom. This does have some story impact, but I feel like it's something I can work around if it's a problem in future content.
But having Morty stop trying to get home, well... that's the main plot. Having him stop trying to get home might have a major conflict with future content. Besides, getting home, or giving up and staying, that's the resolution to the main story, it's the end of the game.
All that being said, I agree, if I was in Morty's shoes, I'd want to stay in this new universe too. And, as I have said in a previous post, when the Unity game does reach it's conclusion (hopefully in the distant future), I do plan to give the player and option to stay if it isn't an option in the Unity version.