I think Amiibo should be allowed for damageless catergories. This is primarily because damageless catergories aim to get number of shines as oppose to the fastest time. Furthermore, an issue with amiibo and non-amiibo catergories together is that amiibo runners are at an advantage. However, amiibo runners in this situation would be at a disadvantage as they would be in fury mode for longer periods of time. Therefore amiibo can be used as a convenience as oppose to giving an advantage.
Imo it's not about having an advantage or disadvantage, it's about fairness and keeping the playing ground equal, since not everyone has an amiibo. If you'd like an advantage amiibo has, with amiibo you go through the game a lot faster, saving minutes to hours in your attempt sessions.