I agree that someone working fewer days per week might be hard to fit into a full-time team culture, but someone working fewer hours per day ought to be pretty easy. For the "fewer hours per day" case, it's just like working across different time zones, which many companies are already well-acclimated to doing -- e.g. you need to schedule all your meetings with this person in the morning because their 5pm is at our 11am.
Someone from EST works 9am-1pm; someone from PST starts work at 9:30am. Daily overlap: 30 minutes.
Yes it could be solved if you want to define core hours in the middle of the day, but I suspect people who want half time work don't view working in the middle of the day every day as the point of the exercise.
