The fact that it is more useful. I gave examples before.
Let's see if I get all of them:
1. Indexing into an array. Okay, all of the formats I gave can do this
quite nicely with at most a simple arithmetic expression, especially in
languages that don't limit you to a 0-n-1 format for an array. I should
also point out that Basic uses 1-based array indexing, so it doesn't
work without such an expression anyways.
2. Boolean comparisons. Okay, flip the sign. Nothing changes, except
that now the implicit arrow actually goes in a direction that actually
makes it visually identical to the implication arrow. Note that nothing
inherent in true versus false as elements of a group of order 2 implies
that one should be greater than the other.
I might also add that nothing inherently implies that 0 should be false
as opposed to true, although you might argue that the group of {true,
false} with the xor operation yields false as the identity element, and
0 is the identity for integers under addition... but under the xnor
operation, true is the identity, and 1 is the identity for integers
under multiplication, so you can clearly argue for other homomorphisms.
In short: I see nothing in your arguments which necessarily implies that
{0, 1} is greater than any other mapping of {true, false} into the integers.