While finding the ESD/PSD of a signal why we always prefer to find it via Auto-correlation function then the square of the FT of the signal?
In the theory of discrete-time random signals, the spectral description of a random process $X[n,s]$ (abbreviated $x[n]$) is often desired, just as it's desired for deterministic signals.
When the frequency of a signal is mentioned at once, the immediate consequent is the Fourier transform of that signal. However, when the signal is random, there is a problem: random processes do not have Fourier transforms. They have infinite energy as the sum
$$ \sum_{n=-\infty}^{\infty} |x[n]|^2 $$
diverges; (as $\lim_{n \to \infty} |x[n]|^2 \neq 0$, which is sufficient to prove that the infinite series cannot converge.) . Thus, the DT Fourier transform of $x[n]$ does not exist:
$$X(\omega) = \sum_{n=-\infty}^{\infty} x[n] e^{-j\omega n} $$ does not converge for any $\omega$.
To overcome this problem for wide-sense stationary random processes, we define and use the auto-correlation sequence (ACS) $r_{xx}[m]$ of the (zero-mean) random process:
$$ r_{xx}[m] = \mathcal{E}\{x[n]x[n+m]^{*} \} ~~~,~~~\text{ for } -\infty &lt; m &lt; \infty$$
The most important property of this ACS (from DTFT point of view) is that it has finite energy (assume aperiodic case) which is sufficient to compute a Fourier transform of it denoted as the power spectral density (PSD) of the WSS random process $x[n]$:
$$ S_{xx}(\omega) = \sum_{m=-\infty}^{\infty} r_{xx}[m] e^{-j \omega m} $$
All these are theory. Because to compute the PSD, you need to know the ACS. But the ACS is related to the PDF (probability density/distribution function) of the random process $x[n]$. And the PDF in practice is not known. In theory (as a part of a homework assignment for example) you can propose a PDF for a given process, and then proceed analytically to compute its ACS and PSD. Yet in practice the signals that you are observing are truly random hence the analytical formulation of their PDF is not exactly known.
So in practice you must find a convenient means of computing the PSD of a partially observed random process (such as a speech given my Martin Luther King). All these approaches are rooted in what is called as Estimation Theory which deals with finding convenient methods of computing certain statistical parameters related with random variables and processes.
One of the methods to estimate the PSD of a random process, relies on estimating its ACS from the observed data, and then taking the Fourier transform of it to reach an estimate of the true PSD. (The true power spectral density relies on the true ACS which is not available but estimated from data).
The other approach, and the more commonly used one, directly estimates the PSD (which is itself a random quantity) from the observed data. The most basic of such direct PSD estimation is known as the periodogram and obtained by computing the Fourier transform of the signal itself;i.e.,
$$I(\omega) = K \cdot |X(\omega)|^2 $$ where $X(\omega)$ is the DTFT of the finite length and finite energy observed random signal $x[n]$,  $K$ is a proper scaling factor and $I(\omega)$ is the periodogram estimate of the PSD.
And this is shows a practical means of computing (actually estimating) the PSD associated with a random process $X[n,s]$ over its partial observations $x[n]$.