Well, to follow your hardware idea, there is one's complement and two's complement notation for integers. One is superior because it makes math easier. Both could be used. In fact the originial cray's used one's complement. Took extra circuitry to take into account the fact that there are 2 zeros in the integer space, though.
A negative zero can be used to represent NUL or NaN, which can be really useful, but not without extra circuitry, like you mention.
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