You could pretty easily have an integer representation using [-127; 128]; 128 being 0x80 of course (all other values being the same as in two's complement). Still would hold that -n == 1 + ~n, zero is all-zeroes, and the property that add/sub needn't care about signed vs unsigned. Only significant difference being that top bit doesn't determine negativeness, though of course it's still "x < 0" in code. (at the hardware level, sign extension & comparisons might also get very slightly more complicated, but that's far outside what typical programmers would need to know)

For most practical purposes outside of low-level stuff all that really matters about two's complement is Don't Get Near 2^(width-1) Or Bad™ Things Happen. Including +128 would even have the benefit of 1<<7 staying positive.