I'm not here to dissuade anyone from their informed opinions on the technique - mostly I was trying to cut through some of the misunderstanding and maybe actually answer OPs question. Like I've said, I haven't yet personally mastered the technique, so I'm really not the best one to defend it. I can agree with you that it doesn't make analysis of complex circuits easy, and it certainly would take some dedicated effort to master the techniques.
I've watched now the 20 Vorpérian's videos (well, with some FF) and he still does not obtain the transfer function in a factored form, but as a ratio of polynomials, and still after the very same tons of algebra. AFAIK no "factored form" for the solution.
Well, I agree there is no way to get away from the fact that a Laplace domain transfer function is a ratio of polynomials. The EET results are factored in the sense that the form of the polynomial is directly a pole and a zero associated with the extra element. I concede that the nEET results seem somewhat more complex, since there is the addition of the cross-coupling terms but I don't know how this could be avoided. I would venture that the algebra is not "the very same" because each term of the solution can be computed in isolation from the others, and because of the Nulled output or Null-Double Injection conditions of the calculations much more of the circuit can "drop out" while you are doing each computation.
I have revisited this method a few times in these 20 years and, definitely, I find it of no value. The supposed fast method is a mechanical, blind, calculation of open/closed impedances and then an equally mechanical and blind construction of expressions from such previous computations. One finally arrives at a solution, but during the process one has gained no insight on why the circuit works as it works. There is no difference in applying this method or applying, equally mechanically and blindly, the matrix method. Or better, mechanically and blindly letting a computer solve it for you.
There are other techniques and tools that not only allow you to solve the circuit, but also give you knowledge about where to touch the circuit to modify some parameter and what to expect from a circuit. Theorems of Miller, Bartlett, Thevenin, quadrupoles, feedback theory, bode plots, network synthesis theory, control theory,… that's the way. Better walk this path and spend no time in delusions.
I agree that for large circuits for which you'd like to compute a specific response, the numerical methods or simulation are best. You loose me when you say that EET is a purely mechanical process which gives no insight into how the circuit works, because that is precisely where it excels. From the start, you pick a reference condition of the circuit and the compute correction terms which model the deviation from that ideal reference state. Each term along the way is a time constant associated with each reactance, or a cross coupling term. Since each term is computed from looking at a circuit, opportunities for simplifying approximation are more abundant. For instance, you may well see that while computing some term two resistances appear in parallel with one much smaller than the other - picking that approximation out of the algebra
after taking a huge determinate would pretty much be a non-starter.
EET/nEET isn't meant to be a substitute for other circuit analysis techniques, and I don't really think anyone would suggest someone should just learn the nEET in lieu of any of the things you list. That said, none of the things you suggest really strike me as incompatible with EET/nEET or as alternatives which would fill the same niche. You could (and probably often should) apply Thevenin/Norton/Bartlett/Miller theorems in the intermediate computations of a nEET analysis. Quadr
ipoles (two port networks) is a way of formatting and using 4 transfer functions, but nEET is a way of deriving any individual transfer function so can be useful in producing a 2-port model. You certainly should analyze your circuits' performance with bode plots and feedback/control theory, but unless you're in a situation where you can do the whole thing numerically you need a transfer function (which the nEET can help with). Network synthesis is not so much a theory, as it is an entire field of techniques. Most are approximations limited to a few useful cases, and generally require some sort of analytical model (i.e transfer function) they can fit to a performance target.
Doesn't all these sound to you as marketing BS?
Somewhat exaggerated maybe, but I don't know if I'd really call it "marketing BS". I don't think there is any subversive profit motive in Vorperian's enthusiasm for the techniques - he probably knows his 18yo circuit analysis books aren't going to crack the NYT best sellers list. My read is that he's had success with these techniques over his academic (Caltech, VT) and professional career (JPL) and is eager to share them. Again, if the techniques aren't for you fair enough but it seems like you're implying some sort of less than genuine motives to Vorperian here which seems unnecessary...