As noted in this previous Stack Exchange question, and many others like it, the transformation from ECI to ECEF (or vice versa) is not a simple process, requiring several steps and considerations (precession, nutation, rotation, polar motion) to arrive at the answer.
However, in my research to create my own version of the process (within the golang coding language), I have noticed that a few widely used space simulation software libraries across various langauges commonly make reference to a single document created in 2001, that boils down the entire process into a single matrix transformation as follows:
$\begin{bmatrix} X \\ Y \\ Z \\ \end{bmatrix}_{ECI} = \begin{bmatrix} C_{\theta g} & -S_{\theta g} & 0 \\ S_{\theta g} & C_{\theta g} & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} \begin{bmatrix} X' \\ Y' \\ Z' \\ \end{bmatrix}_{ECF}$
where
$\theta_g \equiv \text{Greenwich Sidereal Time}$
$\theta_g = \theta_{g0} + \omega(t-t_0)$
$\theta_{g0} \equiv \text{Greenwich hour angle (Greenwich Sidereal Time at the epoch t_0)}$
and C and S refer to cosine and sine, respectively. (original screenshots: 1, 2)
I have seen a direct comparison between the two reference frames before framed in a similar way, but wouldn't this process skip the necessary steps of checking precession, nutation, etc? Or is that only necessary for position/velocity vectors?