Usually you are fine with built-in monitor, yet there are some cases you may need external monitor: 1) voltage ramp-up speed is too slow for MCU brownout circuit 2) MCU brownout voltage treshold shall be changed but MCU do not have means for that, like MSP430 F1/F2 series. Fun fact that AVR users rarely ask this question - because even AtTiny have programmable BOR treshold fuses.
Search internet for "msp430 flash corruption" - you will see people suggesting external monitor as solution
Here's story: Msp430 n00bs sometimes immediately at the startup set internal clock from default ~1 MHz to 16MHz maximum. Thing is that BOR treshold is 0.8V and max allowed frequency at this voltage is 1MHz, for 16MHz at least 3V needed
Obviously "overclocked" msp430 (F1/F2 maybe other as well) may intermittently crash on power-on or even erase some code flash segment. So, if you have facepalm moment and there's no time or MCU resources to fix power-on problem in firmware by simply adding delay or coding "software BOR treshold" using ADC, you can quickly slap-in external 3.0V supervisor.