Note that caffeine does not increase cortisol, it reduces the time your body takes to clear/lower cortisol.
This study linked to below is about developing tolerance to caffeine, but the very first line says: Caffeine increases cortisol secretion in people at rest or undergoing mental stress.
From context, it seems like the intended meaning is that caffeine slows down the cortisol removal, but what was actually written was that it speeds up cortisol removal.
So keeping cortisol up through other means could possibly be beneficial.