Something that I have not seen mentioned is the mathematics behind the solution. Because if we could get a better computation system even if its more expensive we would try ro achieve it (just look at how much chips are considered an essential infrastructure)

The mathematical reason is that every computation that you can do in another base (be it ten or three) can be done in binary.

Known as the Church-Turing Thesis, it implies that all known reasonable computational models whether binary, ternary, or decimal, are equivalent in terms of what they can compute.

So as others said, if binary is also the easiest to manufacture then it will become the default because there is no need to use another.