Problem with power supply ws2812b Arduino 5v vs 12v
The regulator on an Arduino is likely analog.  On this Arduino Uno the regulator is an analog NCP1117ST50T3G as seen in this schematic.  On page 2 of the NCP1117ST50T3G spcification it is stated:


  Internal thermal shutdown protection limits the die temperature to
  approximately 175°C. Proper heatsinking is required to prevent
  activation.


Being an analog power regulator, the difference between the input voltage and the regulated output voltage eventually turns into heat.  This may explain why a 9 volt source may work (drop is only 9V - 5V = 4V) while a 12 volt source may not work (drop is 12V - 5V = 7V).

Consider using a 5 volt power source avoiding the Arduino analog power regulator.  Or, if the only source is 12 volts (for example an automobile), consider using an external switching or buck power supply to convert the 12 volt down to 5 volts and again avoiding the Arduino analog power regulator.  Lastly, it should be possible to still power the Arduino with 12 volts and use its internal power regulator to only power the Arduino. Then independently power the LED strip using an external power regulator.  This last option will likely have the benefit of eliminating the capacitor bank seen in the question and associated components.