The Imms left the repop rates for wands and made the hints coincide with them. Aura has the longest repop timer and thus has the longest amount of time between when it's gathered and when you can get a new hint for it. Both Barrier and Shield can be gathered fairly quickly by comparison. Aura's recharge timer is relatively long and only goes by the time that you're actually in game.

The reason it may feel like more of a time consuming process is because rather than just grabbing your known wand, you have to time the hint so you can learn where the new one's at.

If I could make a suggestion, it would be that you prioritize Aura gathering so you can burn time gathering the other two and put that toward the recharge. That way, you don't feel bored as you're not sitting around as often.