32-bit MC power supply

Why is it that higher bit microcontrollers like the one used on Due work at a supply or logic level of 3.3V?

Because the transistors are usually smaller, and you need to limit the volts/meter to reasonable values because PHYSICS.
(but the smaller transistors are the key; smaller means faster, and cheaper (more transistors per chip), and more complicated (because, room for more transistors per chip.)
Very dense state-of-the-art chips like a Intel Core i7 will typically have a operating voltage of something like 1.2V.