That is right, and you could map the Boolean values to other numbers, e.g. mapping them to +1 and -1 corresponds better to many of the hardware implementation techniques for logic circuits.
However when the use of Boolean algebra is embedded in some bigger theories, there are cases when the mapping to 0 and 1 becomes mandatory, e.g. in relationship with the theory of probabilities or with the theory of binary polynomials, where the logical operations can be mapped to arithmetic or algebraic operations.
The mapping to 0 and 1 is fully exploited in APL and its derivatives, where it enables the concise writing of many kinds of conditional expressions (in a similar manner to how mask registers are used in GPUs and in AVX-512).
However when the use of Boolean algebra is embedded in some bigger theories, there are cases when the mapping to 0 and 1 becomes mandatory, e.g. in relationship with the theory of probabilities or with the theory of binary polynomials, where the logical operations can be mapped to arithmetic or algebraic operations.
The mapping to 0 and 1 is fully exploited in APL and its derivatives, where it enables the concise writing of many kinds of conditional expressions (in a similar manner to how mask registers are used in GPUs and in AVX-512).