A non-integral number like e is obviously of limited utility in physical systems because having e adders in your ALU doesn't make much sense.

3 is closer then 2 to e, which also why ternary arithmetic was attempted for a while, but the massive advantage of binary in terms of implementation (it is much easier and far lower power to use transistors to slam a voltage high or low than keep it somewhere in the middle, and easier to arrange gates to have only on and off as inputs) won in the end.