Since the power spectral density is just the squared of the fourier transform, why is it useful ? Can't I just replace every solution that requires the psd with the fourier transform ?
Power Spectral Density (PSD) is a theoretical construct, required to deal with random processes (signals). It's by definition the Fourier transform of the auto-correlation function (another theoretical construct) of the random processes.
Practical computation (estimation) of the PSD can be done in a number of ways and some of them utilize the way you expressed as the (scaled) square of the magnitude of the Fourier transform of an observed instance of the random process. Such an estimator of the PSD is called as the Periodogram (or its various variants).
Therefore, they are not substitudes for eachother. In practice you can only estimate the true PSD.