I would take burnout days off if I were still employed.
And get laid off again when someone calls the boss and throws a gigantic man-tantrum about being overwhelmed by "all the extra work" they have to do as a result, when they hardly do anything at all.
And while they take the same number of days off in retaliation, leaving me to get everything done (which I do without complaint) in one shift, I start to burn out again, but faster.