My biggest problem with open world games that makes me want fast travel is having to cover the same ground over and over without anything new. That’s a waste of time and boring. Chibi-Robo fixed that for the most part by having a very dynamic world. Within its day/night system and throughout the story you could expect the same location to be substantially different the next day/night. The days also varied, as some characters would change their locations by the day, so retreading the same ground could lead to finding new things.
Some parts did end up with fast travel. Long platforming sections usually only needed to be done once, and then you can kick a rope down or extend a bridge or ladder. The staircases got teleporters. Since nothing really changed in those parts, they acted only as a puzzle or barrier, and once completed could be ignored for the rest of the game. Since traversing them would become a boring waste of time, the fast travel was appreciated.