Yep that's true about the lights, but technically, one can start Cleaving or mass killing by other means for time extensions once Azure is capped and then just build Pearl or any other lights along the way and still see valuable blue pyxis. Since Azure is the quickest to cap, in this scenario, red pyxis could still be used for a good while until everything's capped.

I'm usually farming for TE's over anything else, while the rest of my party is hunting down key items and so forth so my frustrations over the process stem from my experiences trying to mass kill then rummage through dozens of chest in a timely manner. Although, even when amongst my party members while mass killing, there are times when the process slows down killing due to the necessary rummaging. Again, I'm not saying it's not possible to check chest at a decent pace and find what you're looking for here, because we do it everyday, but only that the process can be improved.