Responses

I don't know about Japan, but I know in Korea, it's mostly a money-saving thing. If it's late and the trains aren't running, I could technically take a taxi if I'm that set on getting home, but that'll cost me a good bit more than just crashing with whoever I'm hanging out with until the trains are back up in the morning. If it's not too late, you could take some busses, but you'll need to figure out where to transfer and how many times, and sometimes you have to pay between transfers, so again, it's easier and cheaper to just go to someone's home if they offer.
Do people in Japan use the bus often? I know that the "train stopped running" trope is there to get the couple together but in real life people would try to get on a bus yet they never even seem to consider that option in mangas, sometimes they even walk home instead.