Two's complement encodes -x as ~x + 1 = 2^n - x = -x (mod 2^n) and can therefore be mixed with unsigned for (+, -, *, &, |, ^, ~, <<).
> I think they should be used exclusively when this is needed
The opposite: signed type usage should be kept to a minimum because signed type (and pointer) overflow is UB and will get optimized as such.
C is weakly typed, the basic types are really not to maintain invariants or detect their violation