"The intrinsic base 2 design of the hardware is used to represent numbers in hexadecimal, or base 16. ... So what? If our hardware was configured as base 4 using four distinguishable voltage states, nothing about our computer technology would change." On the contrary, transistors and semiconductors work very well with two basic states (low voltage/ground and high voltage). To truly work at Base 4 would require hardware capable of operating effectively when FOUR voltage states were present, such as Ground, + 5 volts, + 10 volts, + 20 volts.
To imagine that NOTHING about our computer technology would change is to overlook the incredible hurdles facing multi-state electronics at their most fundamental level.
Now, can our Base 2 electronics be used to represent any Base and any state? Of course. Can they "easily" operate at their most fundamental levels in any Base or state? Not now.
That's just a limitation on the implementation of the architecture. You're right, a four-state logic is not practical with current technology. So what? If we had good four-state logic, nothing FUNDAMENTAL would change. Presumably, our computers would get faster by some factor, but so what. Personal computers today are much faster than PCs of 5 years ago (Moore's Law), but nothing FUNDAMENTAL about personal computers has changed.