Logic has left the room. So the guy got transported to different world (nothing new here), "accidentally" found 2 kids, who were slaves, apparently... He somehow had clothes for them, even though he just got transported, but maybe they were from that wind god. He decided to help the kids out of the woods, which is admirable, no argument there, even decided to name them, which is weird, but ok. And then, when he reached a town, no one questioned him being with the kids, even in adventurers' guild, where he was literally asking for IDs...
But that's not all. The guy did not even plan to get the kids to an orphanage. He planned to keep them. Not go to authorities, see if maybe their parents are alive somewhere, figure something else out, but keep them. And kids were fine with that, even though they were slaves, and they were afraid of anyone else. Still not the end of it - because this new random guy with random (not his own) kids is now considered special by a knight, who wants him in some expedition, which sounds like an important event...
Ok, maybe (just maybe), this show is to show how "kids are great" and all, and not something weird, but it is so far removed from reality, that I just can't.
