If, during that slow decay, the feeder supply is restored, as one unaware of this consequence might do in the lab, the system might fail to reset properly, whether there's a supervisor present or not.
not "whether there's a supervisor present or not" If Vdd drop below the supervisors treshold and if that is selected higher then the chips min Vdd (BEWARE - for many chips the max osc freq is lower at that point that at 'normal' Vdd) there WILL be a reset before the chip goes astray.
I remember someones "reset problem" exactly due to the 'BEWARE' above.
Another issue: if the supervisors treshold is selected close to the chips min Vdd and you have RC decoupling you may get into the situation that the chips VDD under some circumstances is lower than the supervisors so, again go haead, blame the supervisor for your bad design.
supervisors work but, as for everything else, not if designed in improperly.

Erik