I have been on again off again doing a fairly intensive write up on this topic going into all the technical details (primarily the hardware side) complete with a fairly full featured/accurate digital recreation of the original MiniMoog VCF in PureData but it is not exactly a priority and progress on that is rather slow.
Edit: I should mention that despite the models not providing the full range of the source they still do provide a full range of their own. You still have your volume and tone controls but they operate on the model, they are not part of the model. They have gotten fairly good at faking things and the tone controls do not sound so much like post recording EQ like they did in the early modeling amps but they also do not interact with the sound like they do in the real amps where changing the bass level does not only change the bass but also affects the gain/distortion/frequency characteristics of the tubes on either side of it as well.
You can also use differentiable DSP to obtain a decent “first pass” approximation using traditional methods, and then rely on the NN to make up the difference afterward. This dramatically reduces the NN parameter count and speeds up computation. I recently tried this on an analog compressor (LA2A) and got 95%+ of the way there with a very small model.
If someone really wanted to use such technologies to be a game changer they would forget about the past and use it to design something new that exploits its strengths in a way that is natural to the musician instead of showing off its weaknesses. The potential of the technology is quite amazing and yet everyone uses it to chase nostalgia.
I'd be very interested to see your approach. So far, the most promising (non-NN) technique I've seen requires taking a symbolic inverse of a sparse matrix, which is just barely possible for a simplified pedal model.
Essentially I break down the circuit into a series of blocks which are easy to model in isolation and then show how the interactions between these blocks are very complex and difficult to model. The starting point is essentially the classic simple moog model with some extra stuff and I add in bits between those blocks to mimic the interactions while comparing it to various digital models of the filter, spice simulations and the real deal.
So I slowly make up a big massive mess of a patch in PureData that eats my entire CPU but does a fairly solid job of the emulation then try and simplify things down to show how each part affects the whole.
Except for Fractal, which models based on the component level.
It’s also not uncommon to create a capture with your pedal plugged into the amp as well. Popular for high gain heavy metal profiles to have a tube screamer in front of the amp. Stuff like the Kemper/Tonex/NAM work great with this kind of setup.
But yes, you get the sound of a specific EQ settings.
When you send through a clean signal, you measure A*B. When you get distortions, you know you’re only measuring B (because they are introduced after A). Then you derive A from that.
Playing feel on the other hand I guess is a different argument. Not sure if that is a placebo though. I do prefer the zero latency of all analog gear.