Is it possible to infer the characteristic curve of a recording device only from (many) recordings? ... with a certain degree of confidence / corridor of accuracy.

What do I mean?
Case in point: There is the huge archive of digitized Edison wax cylinder recordings.

They have annotations, usually year of recording, sometimes producer of recording.
Assuming that, with a good likelihood, grouping the intersection of e.g. one year of recording and a geographic area or even company yields sets of recordings very likely made with the same model / iteration of the technology within a set, given how slow-paced development was back then:

Could one infer the rough frequency response curve of an imaginary "average recording device" of those times from such a narrowed-down set of recordings?

My not exactly DSP expert naive train of thought went like this:


if I have a great enough number of as diverse as possible audio recordings, their sources (i.e. before entering the brass horn to be recorded) should have an average spectrum roughly resembling white noise. This probably means using broadly set up orchestral recordings, not so much "solo singer with background accompaniment", which is weighted too much to vocals in the spectrum.
with a good likelihood of being made on the same model of recording apparatus, an "average spectrum" calculated e.g. with FFTs over the whole set of recordings as described above, should yield the rough response curve of the imaginary recording device


Now, if premise 1. is already wrong, then I'm out of luck.
And 2. could be wrong if the spread of characteristics between individual exemplars of devices of a series is too great - although I guess that's a bit of a question with regards to "what do I need".
Anyway, this was just to show I made some effort thinking about this. If it doesn't work the naive way I am imagining:

Is there a way to do that, only from recordings, without being in possession of an actual device of that type (for measurement)?

The amount of distortion by e.g. saturation within the mechanical recording process can probably not be inferred just from recordings?
Yes, that's definitely possible. The key would be to find recordings where it's reasonably easy to find an acoustic reference. Great candidates for this would be classical or big band recordings. Let's say you have wax cylinder of Beethoven's 5th, you can try to create a reference by analyzing a dozen or so recent recordings of the same piece. The standard deviation would give you a "margin of error" for the reference and than you can simply divide the spectrum of the wax cylinder by the reference spectrum. Repeat for as many recordings as you can find good references for.


  should have an everage spectrum roughly resembling white noise


No. It's certainly not white: closer to pink but with more high end roll off. Hence you need a known good reference to determine exactly what it is.