Yeah, if you suppose that, you can correctly conclude that you only run into overflow if the object is a byte array that fills more than half the address space (though not the entire address space as you say). And that's why this problem remained unnoticed from 01958 or whenever someone first published a correct-on-my-machine binary search until 02006.
But suppose they aren't. Suppose, for example, that you're in Java, where there's no such thing as an unsigned type, and where ints are 32 bits even on a 64-bit machine. Suddenly the move to 64-bit machines around 02006 demonstrates that you have this problem on any array with more than 2³⁰ elements. It's easy to have 2³⁰ elements on a 64-bit machine! Even if they aren't bytes.
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