What are you talking about...Usually the main characters are craving to find a way back to their home world. Even if they were bullied, overworked, had no family...They often have this absurd obsession of wanting to go back. And they 'dive into the new world' simply because they have no other option.
There are some that actually decide to make best of their transfer thinking it's a new start for them...but still, that's because they have no means of going back even if they wanted.
This is fundamentally different and there are few stories like this. Off the top of my head I can think of only one, I believe Chinese, story like this where the main character can move between the two worlds. And I'll say this...this guys seemingly complete lack of interest in the other world is completely unrealistic. Why? Because he still comes to it, still hunts in it...but doesn't try anything more than that. Somebody that wouldn't be interested wouldn't come to it at all. Someone that would be interested would explore more. He does neither. He doesn't react like a living human would.