The goal is to generate a random spectrum that corresponds to a real-valued signal. If the positive and negative frequencies aren’t conjugate-symmetric then the

The goal is to generate a random spectrum that corresponds to a real-valued signal. If the positive and negative frequencies aren’t conjugate-symmetric then the resulting signal after the IDFT will be complex-valued. You can think of it in terms of degrees of freedom. A real-valued length-N signal has N degrees of freedom. A length-N spectrum is complex-valued, meaning 2 degrees of freedom per frequency bin. When you constrain it to be conjugate-symmetric you bring the degrees of freedom back to N, which matches the real-valued signal.