Average PWM Switch Model
Let's see how I can answer your questions:
Q1: yes, the idea behind the PWM model is to replace the switching cell made of the switch and diode by a 2-port circuit in which non-linear time-continuous equations describe the average behavior of the cell while switching. This principle follows that already adopted with the hybrid-\$\pi\$ model of bipolar transistors where you replace the transistor symbol by a linear model and follows the pin arrangement c-b-e when rotating the model to match the original circuit. Whether this is a common-emitter, common-base, common-collector or another arrangement, the hybrid-\$\pi\$ model remains the same: it is an invariant model.
With the PWM switch, it is the same. Once you have identified the switching cell in a switching converter, you plug the PWM switch model as shown in the book or even here, for a recent refresh on the subject. The simplest form of the CCM voltage mode model is a &quot;dc&quot; transformer having a turns ratio \$1:D\$, \$D\$ being the duty ratio. Of course, this is a non-linear equation but the cool thing is that SPICE being a linear solver, when you press AC or TRAN analysis, SPICE will always linearize equations around the computed bias point. So if you plug the simplest form of the model (a \$1:D\$ transformer), you can already simulate and obtain the frequency response of all CCM voltage mode topologies:

Now, if you want to derive a given transfer function, you will have to linearize the \$1:D\$ model into a small-signal model. Once this is done, plug it back into the circuit and work on a linear circuit:

State-Space Averaging is indeed a powerful tool but as you said, it considers the entire converter during the analysis. Should you want to add a resistor somewhere, a front-end filter and so on then you need to re-start from scratch. With the PWM switch, add any linear component like a front-end filter, a post LC filter etc. the model does not change.
Q2: Yes, there are some LTspice models in the page you mention and indeed, they work. Please note that from a voltage mode model, you can easily turn in into a current mode model just by adding an equation linking the control voltage \$V_c\$ to the duty ratio \$D\$. The only thing is that you won't be able to predict sub-harmonic oscillations unless you add a second-order polynomial form in series with the \$D\$ generator. A modeling approach of this technique is described here.