> Wouldn’t you rather answer the questions on your own time without someone else putting you on the spot?

Honestly no, as you might spend loads of time crafting the perfect response, only to find that they hadn't really worded the question in a way that meant your answered what they were really thinking. This happens often enough in in-person interviews as it is, but atleast you can hope to course-correct by looking at how they respond. The lack of time-bounding is a real problem for those who have genuine time-commitments outside of work